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

Percentage Accurate: 95.7% → 97.8%

Time: 3.7s

Alternatives: 11

Speedup: 1.3×

• 41.5% 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: 95.7% 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: 97.8% accurate, 1.3× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-+l+ N/A

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

   6. *-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. +-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lower-*.f64 96.7

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

3. Applied rewrites 96.7%

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

   1. lift-+.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-fma.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. associate-+l+ N/A

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

   8. lift-*.f64 N/A

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

   9. lower-fma.f64 N/A

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

   10. lower-+.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. *-commutative N/A

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

   14. lower-fma.f64 N/A

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

   15. lower-*.f64 N/A

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

   16. *-commutative N/A

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

   17. lower-*.f64 97.1

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

5. Applied rewrites 97.1%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fma.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-+l+ N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 97.8

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

7. Applied rewrites 97.8%

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

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, t, x \cdot y\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(b, a, c \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+275}:\\ \;\;\;\;\mathsf{fma}\left(i, c, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma z t (* x y))) (t_2 (+ (* x y) (* z t))))
   (if (<= t_2 -5e+103)
     t_1
     (if (<= t_2 1e+110)
       (fma b a (* c i))
       (if (<= t_2 1e+275) (fma i c (* 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(z, t, (x * y));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -5e+103) {
		tmp = t_1;
	} else if (t_2 <= 1e+110) {
		tmp = fma(b, a, (c * i));
	} else if (t_2 <= 1e+275) {
		tmp = fma(i, c, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(z, t, Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+103)
		tmp = t_1;
	elseif (t_2 <= 1e+110)
		tmp = fma(b, a, Float64(c * i));
	elseif (t_2 <= 1e+275)
		tmp = fma(i, c, 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[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+103], t$95$1, If[LessEqual[t$95$2, 1e+110], N[(b * a + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+275], N[(i * c + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -5e103 or 9.9999999999999996e274 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 90.9%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

         \[\leadsto z \cdot t + x \cdot y \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 79.6

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

   7. Applied rewrites 79.6%

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

   if -5e103 < (+.f64 (*.f64 x y) (*.f64 z t)) < 1e110

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 88.0

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

   4. Applied rewrites 88.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b, a, c \cdot i\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 77.9

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

   7. Applied rewrites 77.9%

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

   if 1e110 < (+.f64 (*.f64 x y) (*.f64 z t)) < 9.9999999999999996e274

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} + c \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{x} + c \cdot i \]

      2. lower-*.f64 49.3

         \[\leadsto y \cdot \color{blue}{x} + c \cdot i \]

   4. Applied rewrites 49.3%

      \[\leadsto \color{blue}{y \cdot x} + c \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{y \cdot x + c \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto y \cdot x + \color{blue}{c \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{c \cdot i + y \cdot x} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{i \cdot c} + y \cdot x \]

      5. lower-fma.f64 49.3

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 49.3

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

   6. Applied rewrites 49.3%

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

Alternative 3: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, t, x \cdot y\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(b, a, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma z t (* x y))) (t_2 (+ (* x y) (* z t))))
   (if (<= t_2 -5e+103) t_1 (if (<= t_2 2e+131) (fma b a (* c i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(z, t, (x * y));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -5e+103) {
		tmp = t_1;
	} else if (t_2 <= 2e+131) {
		tmp = fma(b, a, (c * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(z, t, Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+103)
		tmp = t_1;
	elseif (t_2 <= 2e+131)
		tmp = fma(b, a, Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+103], t$95$1, If[LessEqual[t$95$2, 2e+131], N[(b * a + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -5e103 or 1.9999999999999998e131 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 86.3

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

   4. Applied rewrites 86.3%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

         \[\leadsto z \cdot t + x \cdot y \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 75.6

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

   7. Applied rewrites 75.6%

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

   if -5e103 < (+.f64 (*.f64 x y) (*.f64 z t)) < 1.9999999999999998e131

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 87.7

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b, a, c \cdot i\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 77.2

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

   7. Applied rewrites 77.2%

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

Alternative 4: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \mathsf{fma}\left(z, t, i \cdot c\right)\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma t z (* y x))))
   (if (<= (* c i) -5e+18)
     (fma y x (fma z t (* i c)))
     (if (<= (* c i) 5e+36) (fma b a t_1) (fma 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 = fma(t, z, (y * x));
	double tmp;
	if ((c * i) <= -5e+18) {
		tmp = fma(y, x, fma(z, t, (i * c)));
	} else if ((c * i) <= 5e+36) {
		tmp = fma(b, a, t_1);
	} else {
		tmp = fma(i, c, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(t, z, Float64(y * x))
	tmp = 0.0
	if (Float64(c * i) <= -5e+18)
		tmp = fma(y, x, fma(z, t, Float64(i * c)));
	elseif (Float64(c * i) <= 5e+36)
		tmp = fma(b, a, t_1);
	else
		tmp = fma(i, c, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5e+18], N[(y * x + N[(z * t + N[(i * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+36], N[(b * a + t$95$1), $MachinePrecision], N[(i * c + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5e18

   1. Initial program 93.9%

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

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 94.7

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

   3. Applied rewrites 94.7%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 97.0

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

   7. Applied rewrites 97.0%

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

   8. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 82.5

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

   10. Applied rewrites 82.5%

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

   if -5e18 < (*.f64 c i) < 4.99999999999999977e36

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 94.1

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

   4. Applied rewrites 94.1%

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

   if 4.99999999999999977e36 < (*.f64 c i)

   1. Initial program 93.5%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 82.5

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

   4. Applied rewrites 82.5%

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

Alternative 5: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, z, y \cdot x\right)\\ t_2 := \mathsf{fma}\left(i, c, t\_1\right)\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma t z (* y x))) (t_2 (fma i c t_1)))
   (if (<= (* c i) -5e+18) t_2 (if (<= (* c i) 5e+36) (fma b a 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 = fma(t, z, (y * x));
	double t_2 = fma(i, c, t_1);
	double tmp;
	if ((c * i) <= -5e+18) {
		tmp = t_2;
	} else if ((c * i) <= 5e+36) {
		tmp = fma(b, a, t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(t, z, Float64(y * x))
	t_2 = fma(i, c, t_1)
	tmp = 0.0
	if (Float64(c * i) <= -5e+18)
		tmp = t_2;
	elseif (Float64(c * i) <= 5e+36)
		tmp = fma(b, a, t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * c + t$95$1), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5e+18], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 5e+36], N[(b * a + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5e18 or 4.99999999999999977e36 < (*.f64 c i)

   1. Initial program 93.7%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 82.5

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

   4. Applied rewrites 82.5%

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

   if -5e18 < (*.f64 c i) < 4.99999999999999977e36

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 94.1

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

   4. Applied rewrites 94.1%

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

Alternative 6: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, c \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2e+294)
   (fma b a (fma i c (* t z)))
   (if (<= (* c i) 4e+101) (fma b a (fma t z (* y x))) (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 tmp;
	if ((c * i) <= -2e+294) {
		tmp = fma(b, a, fma(i, c, (t * z)));
	} else if ((c * i) <= 4e+101) {
		tmp = fma(b, a, fma(t, z, (y * x)));
	} else {
		tmp = fma(y, x, (c * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2e+294)
		tmp = fma(b, a, fma(i, c, Float64(t * z)));
	elseif (Float64(c * i) <= 4e+101)
		tmp = fma(b, a, fma(t, z, Float64(y * x)));
	else
		tmp = fma(y, x, Float64(c * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2e+294], N[(b * a + N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4e+101], N[(b * a + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.00000000000000013e294

   1. Initial program 84.4%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 92.0

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

   4. Applied rewrites 92.0%

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

   if -2.00000000000000013e294 < (*.f64 c i) < 3.9999999999999999e101

   1. Initial program 97.5%

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

   2. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 86.4

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

   4. Applied rewrites 86.4%

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

   if 3.9999999999999999e101 < (*.f64 c i)

   1. Initial program 92.4%

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

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 93.3

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

   3. Applied rewrites 93.3%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 73.0

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

   8. Applied rewrites 73.0%

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

Alternative 7: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(i, c, t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, b \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+103)
   (fma z t (* x y))
   (if (<= (* x y) 2e+183) (fma b a (fma i c (* t z))) (fma y x (* b a)))))

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+103) {
		tmp = fma(z, t, (x * y));
	} else if ((x * y) <= 2e+183) {
		tmp = fma(b, a, fma(i, c, (t * z)));
	} else {
		tmp = fma(y, x, (b * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+103)
		tmp = fma(z, t, Float64(x * y));
	elseif (Float64(x * y) <= 2e+183)
		tmp = fma(b, a, fma(i, c, Float64(t * z)));
	else
		tmp = fma(y, x, Float64(b * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+103], N[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+183], N[(b * a + N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(b * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e103

   1. Initial program 91.7%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 86.2

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

   4. Applied rewrites 86.2%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

         \[\leadsto z \cdot t + x \cdot y \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 74.9

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

   7. Applied rewrites 74.9%

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

   if -5e103 < (*.f64 x y) < 1.99999999999999989e183

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 89.6

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

   4. Applied rewrites 89.6%

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

   if 1.99999999999999989e183 < (*.f64 x y)

   1. Initial program 89.2%

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

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 91.8

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

   3. Applied rewrites 91.8%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 93.6

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 79.3

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

   8. Applied rewrites 79.3%

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

Alternative 8: 43.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+103}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-189}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+137}:\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+103)
   (* y x)
   (if (<= (* x y) -5e-189) (* b a) (if (<= (* x y) 5e+137) (* i c) (* y x)))))

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+103) {
		tmp = y * x;
	} else if ((x * y) <= -5e-189) {
		tmp = b * a;
	} else if ((x * y) <= 5e+137) {
		tmp = i * c;
	} else {
		tmp = y * x;
	}
	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 ((x * y) <= (-5d+103)) then
        tmp = y * x
    else if ((x * y) <= (-5d-189)) then
        tmp = b * a
    else if ((x * y) <= 5d+137) then
        tmp = i * c
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+103) {
		tmp = y * x;
	} else if ((x * y) <= -5e-189) {
		tmp = b * a;
	} else if ((x * y) <= 5e+137) {
		tmp = i * c;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+103:
		tmp = y * x
	elif (x * y) <= -5e-189:
		tmp = b * a
	elif (x * y) <= 5e+137:
		tmp = i * c
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+103)
		tmp = Float64(y * x);
	elseif (Float64(x * y) <= -5e-189)
		tmp = Float64(b * a);
	elseif (Float64(x * y) <= 5e+137)
		tmp = Float64(i * c);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5e+103)
		tmp = y * x;
	elseif ((x * y) <= -5e-189)
		tmp = b * a;
	elseif ((x * y) <= 5e+137)
		tmp = i * c;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+103], N[(y * x), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-189], N[(b * a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+137], N[(i * c), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e103 or 5.0000000000000002e137 < (*.f64 x y)

   1. Initial program 91.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 64.4

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

   4. Applied rewrites 64.4%

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

   if -5e103 < (*.f64 x y) < -4.9999999999999997e-189

   1. Initial program 97.8%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto b \cdot \color{blue}{a} \]

      2. lower-*.f64 30.6

         \[\leadsto b \cdot \color{blue}{a} \]

   4. Applied rewrites 30.6%

      \[\leadsto \color{blue}{b \cdot a} \]

   if -4.9999999999999997e-189 < (*.f64 x y) < 5.0000000000000002e137

   1. Initial program 97.9%

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

   2. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 33.9

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

   4. Applied rewrites 33.9%

      \[\leadsto \color{blue}{i \cdot c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 62.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+294}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2e+294)
   (* i c)
   (if (<= (* c i) 4e+106) (fma z t (* x y)) (* i c))))

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+294) {
		tmp = i * c;
	} else if ((c * i) <= 4e+106) {
		tmp = fma(z, t, (x * y));
	} else {
		tmp = i * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2e+294)
		tmp = Float64(i * c);
	elseif (Float64(c * i) <= 4e+106)
		tmp = fma(z, t, Float64(x * y));
	else
		tmp = Float64(i * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2e+294], N[(i * c), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4e+106], N[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(i * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.00000000000000013e294 or 4.00000000000000036e106 < (*.f64 c i)

   1. Initial program 90.1%

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

   2. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.1

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

   4. Applied rewrites 70.1%

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

   if -2.00000000000000013e294 < (*.f64 c i) < 4.00000000000000036e106

   1. Initial program 97.5%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 72.2

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

   4. Applied rewrites 72.2%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

         \[\leadsto z \cdot t + x \cdot y \]

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 59.8

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

   7. Applied rewrites 59.8%

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

Alternative 10: 41.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+18}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+72}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;i \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5e+18) (* i c) (if (<= (* c i) 5e+72) (* b a) (* i c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5e+18) {
		tmp = i * c;
	} else if ((c * i) <= 5e+72) {
		tmp = b * a;
	} else {
		tmp = i * c;
	}
	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) <= (-5d+18)) then
        tmp = i * c
    else if ((c * i) <= 5d+72) then
        tmp = b * a
    else
        tmp = i * c
    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) <= -5e+18) {
		tmp = i * c;
	} else if ((c * i) <= 5e+72) {
		tmp = b * a;
	} else {
		tmp = i * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5e+18:
		tmp = i * c
	elif (c * i) <= 5e+72:
		tmp = b * a
	else:
		tmp = i * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5e+18)
		tmp = Float64(i * c);
	elseif (Float64(c * i) <= 5e+72)
		tmp = Float64(b * a);
	else
		tmp = Float64(i * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -5e+18)
		tmp = i * c;
	elseif ((c * i) <= 5e+72)
		tmp = b * a;
	else
		tmp = i * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5e+18], N[(i * c), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+72], N[(b * a), $MachinePrecision], N[(i * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5e18 or 4.99999999999999992e72 < (*.f64 c i)

   1. Initial program 93.4%

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

   2. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 54.3

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

   4. Applied rewrites 54.3%

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

   if -5e18 < (*.f64 c i) < 4.99999999999999992e72

   1. Initial program 97.5%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto b \cdot \color{blue}{a} \]

      2. lower-*.f64 32.6

         \[\leadsto b \cdot \color{blue}{a} \]

   4. Applied rewrites 32.6%

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

Alternative 11: 27.0% 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 95.7%

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

2. Taylor expanded in a around inf

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

   1. *-commutative N/A

      \[\leadsto b \cdot \color{blue}{a} \]

   2. lower-*.f64 27.0

      \[\leadsto b \cdot \color{blue}{a} \]

4. Applied rewrites 27.0%

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

Reproduce

herbie shell --seed 2025093 
(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)))