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

Percentage Accurate: 90.5% → 95.5%

Time: 6.2s

Alternatives: 16

Speedup: 1.0×

• 52.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 90.5% accurate, 1.0× speedup

Math

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

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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.5%

   \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
2. 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 95.2%

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

   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 95.5%

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

   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 95.5%

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

3. Applied rewrites 95.5%

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

Alternative 2: 88.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := 2 \cdot \mathsf{fma}\left(z, t, \left(-\left(-\left(-c\right)\right)\right) \cdot \left(i \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, y \cdot x - \left(i \cdot c\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* 2.0 (fma z t (* (- (- (- c))) (* i (fma b c a))))))
       (t_2 (* (* (+ a (* b c)) c) i)))
  (if (<= t_2 -4e+273)
    t_1
    (if (<= t_2 2e+51)
      (* 2.0 (fma z t (- (* y x) (* (* i c) a))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * fma(z, t, (-(-(-c)) * (i * fma(b, c, a))));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -4e+273) {
		tmp = t_1;
	} else if (t_2 <= 2e+51) {
		tmp = 2.0 * fma(z, t, ((y * x) - ((i * c) * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * fma(z, t, Float64(Float64(-Float64(-Float64(-c))) * Float64(i * fma(b, c, a)))))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -4e+273)
		tmp = t_1;
	elseif (t_2 <= 2e+51)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(y * x) - Float64(Float64(i * c) * a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t + N[((-(-(-c))) * N[(i * N[(b * c + a), $MachinePrecision]), $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, -4e+273], t$95$1, If[LessEqual[t$95$2, 2e+51], N[(2.0 * N[(z * t + N[(N[(y * x), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -3.9999999999999998e273 or 2e51 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-neg.f64 N/A

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

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

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

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

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-neg.f64 70.1%

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 70.1%

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

   6. Applied rewrites 70.1%

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

   if -3.9999999999999998e273 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e51

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto 2 \cdot \color{blue}{\left(\left(t \cdot z + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)} \]
   9. 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 73.5%

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

   10. Applied rewrites 73.5%

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

       1. lift--.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. associate--l+ N/A

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

       4. sub-negate-rev N/A

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

       5. *-commutative N/A

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

       6. sub-negate-rev N/A

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

       7. lower-fma.f64 N/A

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

       8. lower--.f64 74.0%

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 74.0%

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

       12. lift-*.f64 N/A

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

       13. *-commutative N/A

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

       14. lower-*.f64 74.0%

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

       15. lift-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lift-*.f64 74.0%

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

   12. Applied rewrites 74.0%

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

Alternative 3: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, y \cdot x - \left(i \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(c, b, a\right), \left(-c\right) \cdot i, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<= (* x y) -5e+74)
  (* 2.0 (fma z t (- (* y x) (* (* i c) a))))
  (if (<= (* x y) 5e+99)
    (* 2.0 (fma (fma c b a) (* (- c) i) (* t z)))
    (* 2.0 (- (fma t z (* x y)) (* a (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+74) {
		tmp = 2.0 * fma(z, t, ((y * x) - ((i * c) * a)));
	} else if ((x * y) <= 5e+99) {
		tmp = 2.0 * fma(fma(c, b, a), (-c * i), (t * z));
	} else {
		tmp = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+74)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(y * x) - Float64(Float64(i * c) * a))));
	elseif (Float64(x * y) <= 5e+99)
		tmp = Float64(2.0 * fma(fma(c, b, a), Float64(Float64(-c) * i), Float64(t * z)));
	else
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+74], N[(2.0 * N[(z * t + N[(N[(y * x), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+99], N[(2.0 * N[(N[(c * b + a), $MachinePrecision] * N[((-c) * i), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999996e74

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto 2 \cdot \color{blue}{\left(\left(t \cdot z + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)} \]
   9. 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 73.5%

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

   10. Applied rewrites 73.5%

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

       1. lift--.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. associate--l+ N/A

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

       4. sub-negate-rev N/A

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

       5. *-commutative N/A

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

       6. sub-negate-rev N/A

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

       7. lower-fma.f64 N/A

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

       8. lower--.f64 74.0%

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 74.0%

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

       12. lift-*.f64 N/A

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

       13. *-commutative N/A

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

       14. lower-*.f64 74.0%

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

       15. lift-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lift-*.f64 74.0%

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

   12. Applied rewrites 74.0%

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

   if -4.9999999999999996e74 < (*.f64 x y) < 5.0000000000000001e99

   1. Initial program 90.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. 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 95.2%

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

      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 95.5%

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

      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 95.5%

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

   3. Applied rewrites 95.5%

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

   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 71.8%

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

   6. Applied rewrites 71.8%

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

   if 5.0000000000000001e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto 2 \cdot \color{blue}{\left(\left(t \cdot z + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)} \]
   9. 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 73.5%

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

   10. Applied rewrites 73.5%

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

Alternative 4: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, y \cdot x - \left(i \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \mathsf{fma}\left(b, c, a\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<= (* x y) -5e+74)
  (* 2.0 (fma z t (- (* y x) (* (* i c) a))))
  (if (<= (* x y) 5e+99)
    (* 2.0 (- (* t z) (* (fma b c a) (* i c))))
    (* 2.0 (- (fma t z (* x y)) (* a (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+74) {
		tmp = 2.0 * fma(z, t, ((y * x) - ((i * c) * a)));
	} else if ((x * y) <= 5e+99) {
		tmp = 2.0 * ((t * z) - (fma(b, c, a) * (i * c)));
	} else {
		tmp = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+74)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(y * x) - Float64(Float64(i * c) * a))));
	elseif (Float64(x * y) <= 5e+99)
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(fma(b, c, a) * Float64(i * c))));
	else
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+74], N[(2.0 * N[(z * t + N[(N[(y * x), $MachinePrecision] - N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+99], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(b * c + a), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999996e74

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto 2 \cdot \color{blue}{\left(\left(t \cdot z + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)} \]
   9. 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 73.5%

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

   10. Applied rewrites 73.5%

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

       1. lift--.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. associate--l+ N/A

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

       4. sub-negate-rev N/A

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

       5. *-commutative N/A

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

       6. sub-negate-rev N/A

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

       7. lower-fma.f64 N/A

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

       8. lower--.f64 74.0%

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 74.0%

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

       12. lift-*.f64 N/A

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

       13. *-commutative N/A

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

       14. lower-*.f64 74.0%

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

       15. lift-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lift-*.f64 74.0%

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

   12. Applied rewrites 74.0%

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

   if -4.9999999999999996e74 < (*.f64 x y) < 5.0000000000000001e99

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 71.5%

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

   6. Applied rewrites 71.5%

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

   if 5.0000000000000001e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto 2 \cdot \color{blue}{\left(\left(t \cdot z + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)} \]
   9. 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 73.5%

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

   10. Applied rewrites 73.5%

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

Alternative 5: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := 2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \mathsf{fma}\left(b, c, a\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* 2.0 (- (fma t z (* x y)) (* a (* c i))))))
  (if (<= (* x y) -5e+74)
    t_1
    (if (<= (* x y) 5e+99)
      (* 2.0 (- (* t z) (* (fma b c a) (* i c))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	double tmp;
	if ((x * y) <= -5e+74) {
		tmp = t_1;
	} else if ((x * y) <= 5e+99) {
		tmp = 2.0 * ((t * z) - (fma(b, c, a) * (i * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))))
	tmp = 0.0
	if (Float64(x * y) <= -5e+74)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+99)
		tmp = Float64(2.0 * Float64(Float64(t * z) - Float64(fma(b, c, a) * Float64(i * c))));
	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[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+74], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+99], N[(2.0 * N[(N[(t * z), $MachinePrecision] - N[(N[(b * c + a), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999996e74 or 5.0000000000000001e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto 2 \cdot \color{blue}{\left(\left(t \cdot z + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)} \]
   9. 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 73.5%

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

   10. Applied rewrites 73.5%

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

   if -4.9999999999999996e74 < (*.f64 x y) < 5.0000000000000001e99

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 71.5%

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

   6. Applied rewrites 71.5%

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

Alternative 6: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \mathsf{fma}\left(b, c, a\right) \cdot \left(i \cdot c\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* 2.0 (- (* t z) (* (fma b c a) (* i c)))))
       (t_2 (* (* (+ a (* b c)) c) i)))
  (if (<= t_2 -5e+90)
    t_1
    (if (<= t_2 2e+51) (* 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 * ((t * z) - (fma(b, c, a) * (i * c)));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -5e+90) {
		tmp = t_1;
	} else if (t_2 <= 2e+51) {
		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(Float64(t * z) - Float64(fma(b, c, a) * Float64(i * c))))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -5e+90)
		tmp = t_1;
	elseif (t_2 <= 2e+51)
		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[(N[(t * z), $MachinePrecision] - N[(N[(b * c + a), $MachinePrecision] * N[(i * c), $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+90], t$95$1, If[LessEqual[t$95$2, 2e+51], 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) < -5.0000000000000004e90 or 2e51 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.8%

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

   4. Applied rewrites 68.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 71.5%

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

   6. Applied rewrites 71.5%

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

   if -5.0000000000000004e90 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e51

   1. Initial program 90.5%

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

   2. 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 54.9%

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

   4. Applied rewrites 54.9%

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

Alternative 7: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot \left(i \cdot -2\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* (* (+ a (* b c)) c) i)))
  (if (<= t_1 -5e+90)
    (* (fma b c a) (* (* i c) -2.0))
    (if (<= t_1 5e+70)
      (* 2.0 (fma t z (* x y)))
      (* (* (fma b c a) c) (* i -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+90) {
		tmp = fma(b, c, a) * ((i * c) * -2.0);
	} else if (t_1 <= 5e+70) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = (fma(b, c, a) * c) * (i * -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+90)
		tmp = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0));
	elseif (t_1 <= 5e+70)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = Float64(Float64(fma(b, c, a) * c) * Float64(i * -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+90], N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+70], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c + a), $MachinePrecision] * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000004e90

   1. Initial program 90.5%

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

   2. 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 47.4%

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

   4. Applied rewrites 47.4%

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   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. add-flip-rev N/A

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

      20. sub-flip N/A

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

      21. lift-*.f64 N/A

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

      22. remove-double-neg N/A

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

      23. lower-fma.f64 N/A

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

   6. Applied rewrites 49.3%

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

   if -5.0000000000000004e90 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000002e70

   1. Initial program 90.5%

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

   2. 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 54.9%

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

   4. Applied rewrites 54.9%

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

   if 5.0000000000000002e70 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. 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 47.4%

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

   4. Applied rewrites 47.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      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. add-flip-rev N/A

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

      18. sub-flip N/A

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

      19. lift-*.f64 N/A

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

      20. remove-double-neg N/A

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

      21. lower-fma.f64 N/A

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

      22. lower-*.f64 47.4%

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

   6. Applied rewrites 47.4%

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

Alternative 8: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot \left(i \cdot -2\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

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 -5e+90)
    t_1
    (if (<= t_2 5e+70) (* 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 <= -5e+90) {
		tmp = t_1;
	} else if (t_2 <= 5e+70) {
		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 <= -5e+90)
		tmp = t_1;
	elseif (t_2 <= 5e+70)
		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, -5e+90], t$95$1, If[LessEqual[t$95$2, 5e+70], 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) < -5.0000000000000004e90 or 5.0000000000000002e70 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. 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 47.4%

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

   4. Applied rewrites 47.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      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. add-flip-rev N/A

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

      18. sub-flip N/A

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

      19. lift-*.f64 N/A

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

      20. remove-double-neg N/A

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

      21. lower-fma.f64 N/A

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

      22. lower-*.f64 47.4%

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

   6. Applied rewrites 47.4%

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

   if -5.0000000000000004e90 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000002e70

   1. Initial program 90.5%

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

   2. 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 54.9%

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

   4. Applied rewrites 54.9%

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

Alternative 9: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+273}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* (* (+ a (* b c)) c) i)))
  (if (<= t_1 -4e+273)
    (* (* b c) (* (* i c) -2.0))
    (if (<= t_1 5e+246)
      (* 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 <= -4e+273) {
		tmp = (b * c) * ((i * c) * -2.0);
	} else if (t_1 <= 5e+246) {
		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 <= -4e+273)
		tmp = Float64(Float64(b * c) * Float64(Float64(i * c) * -2.0));
	elseif (t_1 <= 5e+246)
		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, -4e+273], N[(N[(b * c), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+246], 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) < -3.9999999999999998e273

   1. Initial program 90.5%

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

   2. 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 47.4%

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

   4. Applied rewrites 47.4%

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   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. add-flip-rev N/A

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

      20. sub-flip N/A

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

      21. lift-*.f64 N/A

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

      22. remove-double-neg N/A

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

      23. lower-fma.f64 N/A

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

   6. Applied rewrites 49.3%

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

   7. Taylor expanded in a around 0

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

      1. lower-*.f64 34.2%

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

   9. Applied rewrites 34.2%

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

   if -3.9999999999999998e273 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e246

   1. Initial program 90.5%

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

   2. 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 54.9%

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

   4. Applied rewrites 54.9%

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

   if 4.9999999999999998e246 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. 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 47.4%

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

   4. Applied rewrites 47.4%

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

   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 34.5%

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

   7. Applied rewrites 34.5%

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

Alternative 10: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

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 -4e+273)
    t_1
    (if (<= t_2 5e+246) (* 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 <= -4e+273) {
		tmp = t_1;
	} else if (t_2 <= 5e+246) {
		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 <= -4e+273)
		tmp = t_1;
	elseif (t_2 <= 5e+246)
		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, -4e+273], t$95$1, If[LessEqual[t$95$2, 5e+246], 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) < -3.9999999999999998e273 or 4.9999999999999998e246 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. 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 47.4%

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

   4. Applied rewrites 47.4%

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

   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 34.5%

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

   7. Applied rewrites 34.5%

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

   if -3.9999999999999998e273 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e246

   1. Initial program 90.5%

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

   2. 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 54.9%

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

   4. Applied rewrites 54.9%

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

Alternative 11: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+197}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+133}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot a\right) \cdot c\right) \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* (* (+ a (* b c)) c) i)))
  (if (<= t_1 -1e+197)
    (* -2.0 (* a (* c i)))
    (if (<= t_1 2e+133)
      (* 2.0 (fma t z (* x y)))
      (* (* (* -2.0 a) 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 <= -1e+197) {
		tmp = -2.0 * (a * (c * i));
	} else if (t_1 <= 2e+133) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = ((-2.0 * a) * 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 <= -1e+197)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (t_1 <= 2e+133)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = Float64(Float64(Float64(-2.0 * a) * 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, -1e+197], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+133], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-2.0 * a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

   if -9.9999999999999995e196 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e133

   1. Initial program 90.5%

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

   2. 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 54.9%

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

   4. Applied rewrites 54.9%

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

   if 2e133 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 23.0%

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

   6. Applied rewrites 23.0%

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

Alternative 12: 43.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \left(y + y\right) \cdot x\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+53}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-61}:\\ \;\;\;\;\left(t + t\right) \cdot z\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(\left(i \cdot a\right) \cdot -2\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* (+ y y) x)))
  (if (<= (* x y) -2e+226)
    t_1
    (if (<= (* x y) -5e+53)
      (* -2.0 (* a (* c i)))
      (if (<= (* x y) 2e-61)
        (* (+ t t) z)
        (if (<= (* x y) 5e+99) (* (* (* i a) -2.0) c) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + y) * x;
	double tmp;
	if ((x * y) <= -2e+226) {
		tmp = t_1;
	} else if ((x * y) <= -5e+53) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 2e-61) {
		tmp = (t + t) * z;
	} else if ((x * y) <= 5e+99) {
		tmp = ((i * a) * -2.0) * c;
	} 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 = (y + y) * x
    if ((x * y) <= (-2d+226)) then
        tmp = t_1
    else if ((x * y) <= (-5d+53)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if ((x * y) <= 2d-61) then
        tmp = (t + t) * z
    else if ((x * y) <= 5d+99) then
        tmp = ((i * a) * (-2.0d0)) * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + y) * x;
	double tmp;
	if ((x * y) <= -2e+226) {
		tmp = t_1;
	} else if ((x * y) <= -5e+53) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 2e-61) {
		tmp = (t + t) * z;
	} else if ((x * y) <= 5e+99) {
		tmp = ((i * a) * -2.0) * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y + y) * x
	tmp = 0
	if (x * y) <= -2e+226:
		tmp = t_1
	elif (x * y) <= -5e+53:
		tmp = -2.0 * (a * (c * i))
	elif (x * y) <= 2e-61:
		tmp = (t + t) * z
	elif (x * y) <= 5e+99:
		tmp = ((i * a) * -2.0) * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y + y) * x)
	tmp = 0.0
	if (Float64(x * y) <= -2e+226)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+53)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (Float64(x * y) <= 2e-61)
		tmp = Float64(Float64(t + t) * z);
	elseif (Float64(x * y) <= 5e+99)
		tmp = Float64(Float64(Float64(i * a) * -2.0) * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y + y) * x;
	tmp = 0.0;
	if ((x * y) <= -2e+226)
		tmp = t_1;
	elseif ((x * y) <= -5e+53)
		tmp = -2.0 * (a * (c * i));
	elseif ((x * y) <= 2e-61)
		tmp = (t + t) * z;
	elseif ((x * y) <= 5e+99)
		tmp = ((i * a) * -2.0) * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+226], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+53], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-61], N[(N[(t + t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+99], N[(N[(N[(i * a), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e226 or 5.0000000000000001e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. 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 29.7%

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

   4. Applied rewrites 29.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   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-*l* N/A

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

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.7%

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

   6. Applied rewrites 29.7%

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

   if -1.9999999999999999e226 < (*.f64 x y) < -5.0000000000000004e53

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

   if -5.0000000000000004e53 < (*.f64 x y) < 2.0000000000000001e-61

   1. Initial program 90.5%

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

   2. 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 28.4%

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

   4. Applied rewrites 28.4%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   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. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. count-2-rev N/A

         \[\leadsto \left(t + t\right) \cdot z \]

      6. lower-+.f64 28.4%

         \[\leadsto \left(t + t\right) \cdot z \]

   6. Applied rewrites 28.4%

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

   if 2.0000000000000001e-61 < (*.f64 x y) < 5.0000000000000001e99

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 21.6%

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

   6. Applied rewrites 21.6%

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

Alternative 13: 42.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \left(y + y\right) \cdot x\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+53}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-61}:\\ \;\;\;\;\left(t + t\right) \cdot z\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(\left(-2 \cdot a\right) \cdot c\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* (+ y y) x)))
  (if (<= (* x y) -2e+226)
    t_1
    (if (<= (* x y) -5e+53)
      (* -2.0 (* a (* c i)))
      (if (<= (* x y) 2e-61)
        (* (+ t t) z)
        (if (<= (* x y) 5e+99) (* (* (* -2.0 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 = (y + y) * x;
	double tmp;
	if ((x * y) <= -2e+226) {
		tmp = t_1;
	} else if ((x * y) <= -5e+53) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 2e-61) {
		tmp = (t + t) * z;
	} else if ((x * y) <= 5e+99) {
		tmp = ((-2.0 * a) * c) * i;
	} 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 = (y + y) * x
    if ((x * y) <= (-2d+226)) then
        tmp = t_1
    else if ((x * y) <= (-5d+53)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if ((x * y) <= 2d-61) then
        tmp = (t + t) * z
    else if ((x * y) <= 5d+99) then
        tmp = (((-2.0d0) * a) * c) * i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + y) * x;
	double tmp;
	if ((x * y) <= -2e+226) {
		tmp = t_1;
	} else if ((x * y) <= -5e+53) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 2e-61) {
		tmp = (t + t) * z;
	} else if ((x * y) <= 5e+99) {
		tmp = ((-2.0 * a) * c) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y + y) * x
	tmp = 0
	if (x * y) <= -2e+226:
		tmp = t_1
	elif (x * y) <= -5e+53:
		tmp = -2.0 * (a * (c * i))
	elif (x * y) <= 2e-61:
		tmp = (t + t) * z
	elif (x * y) <= 5e+99:
		tmp = ((-2.0 * a) * c) * i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y + y) * x)
	tmp = 0.0
	if (Float64(x * y) <= -2e+226)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+53)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (Float64(x * y) <= 2e-61)
		tmp = Float64(Float64(t + t) * z);
	elseif (Float64(x * y) <= 5e+99)
		tmp = Float64(Float64(Float64(-2.0 * a) * c) * i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y + y) * x;
	tmp = 0.0;
	if ((x * y) <= -2e+226)
		tmp = t_1;
	elseif ((x * y) <= -5e+53)
		tmp = -2.0 * (a * (c * i));
	elseif ((x * y) <= 2e-61)
		tmp = (t + t) * z;
	elseif ((x * y) <= 5e+99)
		tmp = ((-2.0 * a) * c) * i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+226], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+53], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-61], N[(N[(t + t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+99], N[(N[(N[(-2.0 * a), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e226 or 5.0000000000000001e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. 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 29.7%

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

   4. Applied rewrites 29.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   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-*l* N/A

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

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.7%

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

   6. Applied rewrites 29.7%

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

   if -1.9999999999999999e226 < (*.f64 x y) < -5.0000000000000004e53

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

   if -5.0000000000000004e53 < (*.f64 x y) < 2.0000000000000001e-61

   1. Initial program 90.5%

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

   2. 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 28.4%

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

   4. Applied rewrites 28.4%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   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. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. count-2-rev N/A

         \[\leadsto \left(t + t\right) \cdot z \]

      6. lower-+.f64 28.4%

         \[\leadsto \left(t + t\right) \cdot z \]

   6. Applied rewrites 28.4%

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

   if 2.0000000000000001e-61 < (*.f64 x y) < 5.0000000000000001e99

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 23.0%

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

   6. Applied rewrites 23.0%

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

Alternative 14: 42.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(y + y\right) \cdot x\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+226}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-61}:\\ \;\;\;\;\left(t + t\right) \cdot z\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* -2.0 (* a (* c i)))) (t_2 (* (+ y y) x)))
  (if (<= (* x y) -2e+226)
    t_2
    (if (<= (* x y) -5e+53)
      t_1
      (if (<= (* x y) 2e-61)
        (* (+ t t) z)
        (if (<= (* x y) 5e+99) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = (y + y) * x;
	double tmp;
	if ((x * y) <= -2e+226) {
		tmp = t_2;
	} else if ((x * y) <= -5e+53) {
		tmp = t_1;
	} else if ((x * y) <= 2e-61) {
		tmp = (t + t) * z;
	} else if ((x * y) <= 5e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (-2.0d0) * (a * (c * i))
    t_2 = (y + y) * x
    if ((x * y) <= (-2d+226)) then
        tmp = t_2
    else if ((x * y) <= (-5d+53)) then
        tmp = t_1
    else if ((x * y) <= 2d-61) then
        tmp = (t + t) * z
    else if ((x * y) <= 5d+99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = (y + y) * x;
	double tmp;
	if ((x * y) <= -2e+226) {
		tmp = t_2;
	} else if ((x * y) <= -5e+53) {
		tmp = t_1;
	} else if ((x * y) <= 2e-61) {
		tmp = (t + t) * z;
	} else if ((x * y) <= 5e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (a * (c * i))
	t_2 = (y + y) * x
	tmp = 0
	if (x * y) <= -2e+226:
		tmp = t_2
	elif (x * y) <= -5e+53:
		tmp = t_1
	elif (x * y) <= 2e-61:
		tmp = (t + t) * z
	elif (x * y) <= 5e+99:
		tmp = t_1
	else:
		tmp = t_2
	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(y + y) * x)
	tmp = 0.0
	if (Float64(x * y) <= -2e+226)
		tmp = t_2;
	elseif (Float64(x * y) <= -5e+53)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-61)
		tmp = Float64(Float64(t + t) * z);
	elseif (Float64(x * y) <= 5e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (a * (c * i));
	t_2 = (y + y) * x;
	tmp = 0.0;
	if ((x * y) <= -2e+226)
		tmp = t_2;
	elseif ((x * y) <= -5e+53)
		tmp = t_1;
	elseif ((x * y) <= 2e-61)
		tmp = (t + t) * z;
	elseif ((x * y) <= 5e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+226], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5e+53], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-61], N[(N[(t + t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.9999999999999999e226 or 5.0000000000000001e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. 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 29.7%

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

   4. Applied rewrites 29.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   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-*l* N/A

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

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.7%

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

   6. Applied rewrites 29.7%

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

   if -1.9999999999999999e226 < (*.f64 x y) < -5.0000000000000004e53 or 2.0000000000000001e-61 < (*.f64 x y) < 5.0000000000000001e99

   1. Initial program 90.5%

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

   2. 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 25.1%

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

   4. Applied rewrites 25.1%

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

   if -5.0000000000000004e53 < (*.f64 x y) < 2.0000000000000001e-61

   1. Initial program 90.5%

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

   2. 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 28.4%

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

   4. Applied rewrites 28.4%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   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. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. count-2-rev N/A

         \[\leadsto \left(t + t\right) \cdot z \]

      6. lower-+.f64 28.4%

         \[\leadsto \left(t + t\right) \cdot z \]

   6. Applied rewrites 28.4%

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

Alternative 15: 41.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := \left(y + y\right) \cdot x\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+100}:\\ \;\;\;\;\left(t + t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* (+ y y) x)))
  (if (<= (* x y) -4e+95)
    t_1
    (if (<= (* x y) 2e+100) (* (+ t t) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + y) * x;
	double tmp;
	if ((x * y) <= -4e+95) {
		tmp = t_1;
	} else if ((x * y) <= 2e+100) {
		tmp = (t + t) * z;
	} 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 = (y + y) * x
    if ((x * y) <= (-4d+95)) then
        tmp = t_1
    else if ((x * y) <= 2d+100) then
        tmp = (t + t) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y + y) * x;
	double tmp;
	if ((x * y) <= -4e+95) {
		tmp = t_1;
	} else if ((x * y) <= 2e+100) {
		tmp = (t + t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y + y) * x
	tmp = 0
	if (x * y) <= -4e+95:
		tmp = t_1
	elif (x * y) <= 2e+100:
		tmp = (t + t) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y + y) * x)
	tmp = 0.0
	if (Float64(x * y) <= -4e+95)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+100)
		tmp = Float64(Float64(t + t) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y + y) * x;
	tmp = 0.0;
	if ((x * y) <= -4e+95)
		tmp = t_1;
	elseif ((x * y) <= 2e+100)
		tmp = (t + t) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+95], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+100], N[(N[(t + t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.0000000000000001e95 or 2e100 < (*.f64 x y)

   1. Initial program 90.5%

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

   2. 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 29.7%

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

   4. Applied rewrites 29.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   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-*l* N/A

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

      5. count-2 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 29.7%

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

   6. Applied rewrites 29.7%

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

   if -4.0000000000000001e95 < (*.f64 x y) < 2e100

   1. Initial program 90.5%

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

   2. 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 28.4%

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

   4. Applied rewrites 28.4%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   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. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. count-2-rev N/A

         \[\leadsto \left(t + t\right) \cdot z \]

      6. lower-+.f64 28.4%

         \[\leadsto \left(t + t\right) \cdot z \]

   6. Applied rewrites 28.4%

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

Alternative 16: 28.4% accurate, 4.1× speedup

Math

\[\left(t + t\right) \cdot z \]

FPCore

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

C

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

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 = (t + t) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

2. 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 28.4%

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

4. Applied rewrites 28.4%

   \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
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. associate-*r* N/A

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

   4. lower-*.f64 N/A

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

   5. count-2-rev N/A

      \[\leadsto \left(t + t\right) \cdot z \]

   6. lower-+.f64 28.4%

      \[\leadsto \left(t + t\right) \cdot z \]

6. Applied rewrites 28.4%

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

Reproduce

herbie shell --seed 2025212 
(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))))