Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.9% → 97.9%

Time: 4.7s

Alternatives: 9

Speedup: 1.3×

• 41.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, \mathsf{fma}\left(t, z, \mathsf{fma}\left(i, c, b \cdot a\right)\right)\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

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

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

   4. lift-+.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. associate-+l+ N/A

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

   7. associate--l+ N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

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

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

   11. lift-*.f64 N/A

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

   12. lower-fma.f64 N/A

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

   13. associate-+r+ N/A

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

   14. lift-*.f64 N/A

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

   15. remove-double-neg N/A

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

   16. remove-double-neg N/A

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

   17. *-commutative N/A

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

   18. lower-fma.f64 N/A

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

   19. +-commutative N/A

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

4. Applied rewrites 99.6%

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

Alternative 2: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-319}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(i, c, t \cdot z\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i c (* a b))))
   (if (<= (* x y) -4e+88)
     (fma y x (* a b))
     (if (<= (* x y) 5e-319)
       t_1
       (if (<= (* x y) 1e+40)
         (fma i c (* t z))
         (if (<= (* x y) 1e+113) t_1 (fma y x (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, c, (a * b));
	double tmp;
	if ((x * y) <= -4e+88) {
		tmp = fma(y, x, (a * b));
	} else if ((x * y) <= 5e-319) {
		tmp = t_1;
	} else if ((x * y) <= 1e+40) {
		tmp = fma(i, c, (t * z));
	} else if ((x * y) <= 1e+113) {
		tmp = t_1;
	} else {
		tmp = fma(y, x, (c * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, c, Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -4e+88)
		tmp = fma(y, x, Float64(a * b));
	elseif (Float64(x * y) <= 5e-319)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+40)
		tmp = fma(i, c, Float64(t * z));
	elseif (Float64(x * y) <= 1e+113)
		tmp = t_1;
	else
		tmp = fma(y, x, Float64(c * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+88], N[(y * x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-319], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+40], N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+113], t$95$1, N[(y * x + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.99999999999999984e88

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. associate-+r+ N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. remove-double-neg N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 89.3%

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

   if -3.99999999999999984e88 < (*.f64 x y) < 4.9999937e-319 or 1.00000000000000003e40 < (*.f64 x y) < 1e113

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 79.2%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 80.0

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

   7. Applied rewrites 80.0%

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

   if 4.9999937e-319 < (*.f64 x y) < 1.00000000000000003e40

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 55.8

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

   7. Applied rewrites 55.8%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 74.0%

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

   if 1e113 < (*.f64 x y)

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. associate-+r+ N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. remove-double-neg N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in c around inf

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

   7. Applied rewrites 84.5%

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

Alternative 3: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+159}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-319}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(i, c, t \cdot z\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i c (* a b))))
   (if (<= (* x y) -2e+159)
     (* y x)
     (if (<= (* x y) 5e-319)
       t_1
       (if (<= (* x y) 1e+40)
         (fma i c (* t z))
         (if (<= (* x y) 1e+185) t_1 (* y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, c, (a * b));
	double tmp;
	if ((x * y) <= -2e+159) {
		tmp = y * x;
	} else if ((x * y) <= 5e-319) {
		tmp = t_1;
	} else if ((x * y) <= 1e+40) {
		tmp = fma(i, c, (t * z));
	} else if ((x * y) <= 1e+185) {
		tmp = t_1;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, c, Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -2e+159)
		tmp = Float64(y * x);
	elseif (Float64(x * y) <= 5e-319)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+40)
		tmp = fma(i, c, Float64(t * z));
	elseif (Float64(x * y) <= 1e+185)
		tmp = t_1;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+159], N[(y * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-319], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+40], N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+185], t$95$1, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.9999999999999999e159 or 9.9999999999999998e184 < (*.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.5%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -1.9999999999999999e159 < (*.f64 x y) < 4.9999937e-319 or 1.00000000000000003e40 < (*.f64 x y) < 9.9999999999999998e184

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 76.1%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 76.8

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

   7. Applied rewrites 76.8%

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

   if 4.9999937e-319 < (*.f64 x y) < 1.00000000000000003e40

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 55.8

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

   7. Applied rewrites 55.8%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 74.0%

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

Alternative 4: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+142} \lor \neg \left(t\_1 \leq 10^{+185}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= t_1 -5e+142) (not (<= t_1 1e+185)))
     (fma y x (* z t))
     (fma i c (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((t_1 <= -5e+142) || !(t_1 <= 1e+185)) {
		tmp = fma(y, x, (z * t));
	} else {
		tmp = fma(i, c, (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -5e+142) || !(t_1 <= 1e+185))
		tmp = fma(y, x, Float64(z * t));
	else
		tmp = fma(i, c, Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+142], N[Not[LessEqual[t$95$1, 1e+185]], $MachinePrecision]], N[(y * x + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000001e142 or 9.9999999999999998e184 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 95.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. associate-+r+ N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. remove-double-neg N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 80.4%

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

   if -5.0000000000000001e142 < (+.f64 (*.f64 x y) (*.f64 z t)) < 9.9999999999999998e184

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 82.4%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 83.1

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

   7. Applied rewrites 83.1%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq -5 \cdot 10^{+142} \lor \neg \left(x \cdot y + z \cdot t \leq 10^{+185}\right):\\ \;\;\;\;\mathsf{fma}\left(y, x, z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, x, a \cdot b\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-319}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(i, c, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y x (* a b))))
   (if (<= (* x y) -4e+88)
     t_1
     (if (<= (* x y) 5e-319)
       (fma i c (* a b))
       (if (<= (* x y) 2e+87) (fma i c (* t z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, x, (a * b));
	double tmp;
	if ((x * y) <= -4e+88) {
		tmp = t_1;
	} else if ((x * y) <= 5e-319) {
		tmp = fma(i, c, (a * b));
	} else if ((x * y) <= 2e+87) {
		tmp = fma(i, c, (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, x, Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -4e+88)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-319)
		tmp = fma(i, c, Float64(a * b));
	elseif (Float64(x * y) <= 2e+87)
		tmp = fma(i, c, Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * x + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+88], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-319], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+87], N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999984e88 or 1.9999999999999999e87 < (*.f64 x y)

   1. Initial program 97.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. associate-+r+ N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. remove-double-neg N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 82.8%

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

   if -3.99999999999999984e88 < (*.f64 x y) < 4.9999937e-319

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 77.4%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 78.3

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

   7. Applied rewrites 78.3%

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

   if 4.9999937e-319 < (*.f64 x y) < 1.9999999999999999e87

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 62.4%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 62.4

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

   7. Applied rewrites 62.4%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 74.1%

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

Alternative 6: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(i, c, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5e+128)
   (fma i c (* a b))
   (if (<= (* a b) 5e+180) (fma i c (fma t z (* y x))) (fma y x (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+128) {
		tmp = fma(i, c, (a * b));
	} else if ((a * b) <= 5e+180) {
		tmp = fma(i, c, fma(t, z, (y * x)));
	} else {
		tmp = fma(y, x, (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5e+128)
		tmp = fma(i, c, Float64(a * b));
	elseif (Float64(a * b) <= 5e+180)
		tmp = fma(i, c, fma(t, z, Float64(y * x)));
	else
		tmp = fma(y, x, Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+128], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+180], N[(i * c + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5e128

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 88.7%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 91.0

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

   7. Applied rewrites 91.0%

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

   if -5e128 < (*.f64 a b) < 4.9999999999999996e180

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 89.9%

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

   if 4.9999999999999996e180 < (*.f64 a b)

   1. Initial program 93.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate--l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. associate-+r+ N/A

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

      14. lift-*.f64 N/A

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

      15. remove-double-neg N/A

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

      16. remove-double-neg N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 90.6%

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

Alternative 7: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+159} \lor \neg \left(x \cdot y \leq 10^{+185}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+159) (not (<= (* x y) 1e+185)))
   (* y x)
   (fma i c (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+159) || !((x * y) <= 1e+185)) {
		tmp = y * x;
	} else {
		tmp = fma(i, c, (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+159) || !(Float64(x * y) <= 1e+185))
		tmp = Float64(y * x);
	else
		tmp = fma(i, c, Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+159], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+185]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(i * c + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e159 or 9.9999999999999998e184 < (*.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.5%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -1.9999999999999999e159 < (*.f64 x y) < 9.9999999999999998e184

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 70.2%

      \[\leadsto \color{blue}{b \cdot a} + c \cdot i \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{b \cdot a + c \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + b \cdot a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot i} + b \cdot a \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + b \cdot a \]

      5. lower-fma.f64 70.7

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

   7. Applied rewrites 70.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+159} \lor \neg \left(x \cdot y \leq 10^{+185}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+47} \lor \neg \left(c \cdot i \leq 10^{+56}\right):\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2e+47) (not (<= (* c i) 1e+56))) (* i c) (* b a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2e+47) || !((c * i) <= 1e+56)) {
		tmp = i * c;
	} else {
		tmp = b * a;
	}
	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) :: tmp
    if (((c * i) <= (-2d+47)) .or. (.not. ((c * i) <= 1d+56))) then
        tmp = i * c
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2e+47) || !((c * i) <= 1e+56)) {
		tmp = i * c;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2e+47) or not ((c * i) <= 1e+56):
		tmp = i * c
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2e+47) || !(Float64(c * i) <= 1e+56))
		tmp = Float64(i * c);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -2e+47) || ~(((c * i) <= 1e+56)))
		tmp = i * c;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2e+47], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1e+56]], $MachinePrecision]], N[(i * c), $MachinePrecision], N[(b * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.0000000000000001e47 or 1.00000000000000009e56 < (*.f64 c i)

   1. Initial program 96.4%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{i \cdot c} \]

   if -2.0000000000000001e47 < (*.f64 c i) < 1.00000000000000009e56

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

   5. Applied rewrites 42.3%

      \[\leadsto \color{blue}{b \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+47} \lor \neg \left(c \cdot i \leq 10^{+56}\right):\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 27.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ b \cdot a \end{array} \]

FPCore

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

C

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

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 = b * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot b} \]
4. Step-by-step derivation

5. Applied rewrites 31.0%

   \[\leadsto \color{blue}{b \cdot a} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025019 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))