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

Percentage Accurate: 95.6% → 97.4%

Time: 7.4s

Alternatives: 11

Speedup: 0.5×

• 42.1% 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: 95.6% 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: 97.4% accurate, 0.5× speedup

Math

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

FPCore

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

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)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(i, c, (t * z));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 50.0

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 58.3

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

   8. Applied rewrites 58.3%

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

Alternative 2: 41.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{+164}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;c \cdot i \leq 5000000:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;c \cdot i \leq 10^{+131}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;i \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+230)
   (* i c)
   (if (<= (* c i) -5e+164)
     (* b a)
     (if (<= (* c i) 5000000.0)
       (* t z)
       (if (<= (* c i) 1e+131) (* y x) (* 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) <= -1e+230) {
		tmp = i * c;
	} else if ((c * i) <= -5e+164) {
		tmp = b * a;
	} else if ((c * i) <= 5000000.0) {
		tmp = t * z;
	} else if ((c * i) <= 1e+131) {
		tmp = y * x;
	} 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) <= (-1d+230)) then
        tmp = i * c
    else if ((c * i) <= (-5d+164)) then
        tmp = b * a
    else if ((c * i) <= 5000000.0d0) then
        tmp = t * z
    else if ((c * i) <= 1d+131) then
        tmp = y * x
    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) <= -1e+230) {
		tmp = i * c;
	} else if ((c * i) <= -5e+164) {
		tmp = b * a;
	} else if ((c * i) <= 5000000.0) {
		tmp = t * z;
	} else if ((c * i) <= 1e+131) {
		tmp = y * x;
	} else {
		tmp = i * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+230:
		tmp = i * c
	elif (c * i) <= -5e+164:
		tmp = b * a
	elif (c * i) <= 5000000.0:
		tmp = t * z
	elif (c * i) <= 1e+131:
		tmp = y * x
	else:
		tmp = i * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+230)
		tmp = Float64(i * c);
	elseif (Float64(c * i) <= -5e+164)
		tmp = Float64(b * a);
	elseif (Float64(c * i) <= 5000000.0)
		tmp = Float64(t * z);
	elseif (Float64(c * i) <= 1e+131)
		tmp = Float64(y * x);
	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) <= -1e+230)
		tmp = i * c;
	elseif ((c * i) <= -5e+164)
		tmp = b * a;
	elseif ((c * i) <= 5000000.0)
		tmp = t * z;
	elseif ((c * i) <= 1e+131)
		tmp = y * x;
	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], -1e+230], N[(i * c), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5e+164], N[(b * a), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5000000.0], N[(t * z), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+131], N[(y * x), $MachinePrecision], N[(i * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.0000000000000001e230 or 9.9999999999999991e130 < (*.f64 c i)

   1. Initial program 88.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if -1.0000000000000001e230 < (*.f64 c i) < -4.9999999999999995e164

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

   if -4.9999999999999995e164 < (*.f64 c i) < 5e6

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 44.4

         \[\leadsto t \cdot \color{blue}{z} \]

   5. Applied rewrites 44.4%

      \[\leadsto \color{blue}{t \cdot z} \]

   if 5e6 < (*.f64 c i) < 9.9999999999999991e130

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.0

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

   5. Applied rewrites 56.0%

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

Alternative 3: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+157} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+107}\right):\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= t_1 -1e+157) (not (<= t_1 2e+107)))
     (fma t z (* y x))
     (fma i c (* b a)))))

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 <= -1e+157) || !(t_1 <= 2e+107)) {
		tmp = fma(t, z, (y * x));
	} else {
		tmp = fma(i, c, (b * a));
	}
	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 <= -1e+157) || !(t_1 <= 2e+107))
		tmp = fma(t, z, Float64(y * x));
	else
		tmp = fma(i, c, Float64(b * a));
	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, -1e+157], N[Not[LessEqual[t$95$1, 2e+107]], $MachinePrecision]], N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(i * c + N[(b * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -9.99999999999999983e156 or 1.9999999999999999e107 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 92.6%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 88.9

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 78.5

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

   8. Applied rewrites 78.5%

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

   if -9.99999999999999983e156 < (+.f64 (*.f64 x y) (*.f64 z t)) < 1.9999999999999999e107

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.8

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

   5. Applied rewrites 76.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative 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%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq -1 \cdot 10^{+157} \lor \neg \left(x \cdot y + z \cdot t \leq 2 \cdot 10^{+107}\right):\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, c, t \cdot z\right)\\ \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;c \cdot i \leq 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i c (* t z))))
   (if (<= (* c i) -1e+230)
     t_1
     (if (<= (* c i) -2e+176)
       (fma b a (* y x))
       (if (<= (* c i) 1e+131) (fma t z (* y x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, c, (t * z));
	double tmp;
	if ((c * i) <= -1e+230) {
		tmp = t_1;
	} else if ((c * i) <= -2e+176) {
		tmp = fma(b, a, (y * x));
	} else if ((c * i) <= 1e+131) {
		tmp = fma(t, z, (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, c, Float64(t * z))
	tmp = 0.0
	if (Float64(c * i) <= -1e+230)
		tmp = t_1;
	elseif (Float64(c * i) <= -2e+176)
		tmp = fma(b, a, Float64(y * x));
	elseif (Float64(c * i) <= 1e+131)
		tmp = fma(t, z, Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * c + N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1e+230], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -2e+176], N[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+131], N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.0000000000000001e230 or 9.9999999999999991e130 < (*.f64 c i)

   1. Initial program 88.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 84.8

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 83.4

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

   8. Applied rewrites 83.4%

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

   if -1.0000000000000001e230 < (*.f64 c i) < -2e176

   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 c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 90.6

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

   8. Applied rewrites 90.6%

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

   if -2e176 < (*.f64 c i) < 9.9999999999999991e130

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 71.0

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

   8. Applied rewrites 71.0%

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

Alternative 5: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y \cdot x\right)\\ \mathbf{elif}\;c \cdot i \leq 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+230)
   (* i c)
   (if (<= (* c i) -2e+176)
     (fma b a (* y x))
     (if (<= (* c i) 1e+139) (fma t z (* y x)) (* 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) <= -1e+230) {
		tmp = i * c;
	} else if ((c * i) <= -2e+176) {
		tmp = fma(b, a, (y * x));
	} else if ((c * i) <= 1e+139) {
		tmp = fma(t, z, (y * x));
	} else {
		tmp = i * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+230)
		tmp = Float64(i * c);
	elseif (Float64(c * i) <= -2e+176)
		tmp = fma(b, a, Float64(y * x));
	elseif (Float64(c * i) <= 1e+139)
		tmp = fma(t, z, Float64(y * x));
	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], -1e+230], N[(i * c), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2e+176], N[(b * a + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+139], N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(i * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.0000000000000001e230 or 1.00000000000000003e139 < (*.f64 c i)

   1. Initial program 88.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -1.0000000000000001e230 < (*.f64 c i) < -2e176

   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 c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 90.6

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

   8. Applied rewrites 90.6%

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

   if -2e176 < (*.f64 c i) < 1.00000000000000003e139

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 70.6

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

   8. Applied rewrites 70.6%

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

Alternative 6: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230} \lor \neg \left(c \cdot i \leq 10^{+131}\right):\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1e+230) (not (<= (* c i) 1e+131)))
   (fma i c (* b a))
   (fma b a (fma t z (* y x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1e+230) || !((c * i) <= 1e+131)) {
		tmp = fma(i, c, (b * a));
	} else {
		tmp = fma(b, a, fma(t, z, (y * x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1e+230) || !(Float64(c * i) <= 1e+131))
		tmp = fma(i, c, Float64(b * a));
	else
		tmp = fma(b, a, fma(t, z, Float64(y * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1e+230], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1e+131]], $MachinePrecision]], N[(i * c + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(b * a + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.0000000000000001e230 or 9.9999999999999991e130 < (*.f64 c i)

   1. Initial program 88.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 86.5

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

   5. Applied rewrites 86.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative 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 87.9

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

   7. Applied rewrites 87.9%

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

   if -1.0000000000000001e230 < (*.f64 c i) < 9.9999999999999991e130

   1. Initial program 97.8%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 91.1

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

   5. Applied rewrites 91.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230} \lor \neg \left(c \cdot i \leq 10^{+131}\right):\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, \mathsf{fma}\left(t, z, y \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230}:\\ \;\;\;\;\mathsf{fma}\left(i, c, b \cdot a\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(b, a, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma t z (* y x))))
   (if (<= (* c i) -1e+230)
     (fma i c (* b a))
     (if (<= (* c i) 5e+64) (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) <= -1e+230) {
		tmp = fma(i, c, (b * a));
	} else if ((c * i) <= 5e+64) {
		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) <= -1e+230)
		tmp = fma(i, c, Float64(b * a));
	elseif (Float64(c * i) <= 5e+64)
		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], -1e+230], N[(i * c + N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+64], 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) < -1.0000000000000001e230

   1. Initial program 89.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.0

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

   5. Applied rewrites 87.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative 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 87.0

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

   7. Applied rewrites 87.0%

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

   if -1.0000000000000001e230 < (*.f64 c i) < 5e64

   1. Initial program 97.7%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{a \cdot b + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 92.7

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

   5. Applied rewrites 92.7%

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

   if 5e64 < (*.f64 c i)

   1. Initial program 90.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 87.4

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

   5. Applied rewrites 87.4%

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

Alternative 8: 41.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230}:\\ \;\;\;\;i \cdot c\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{+164}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;c \cdot i \leq 10^{+78}:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;i \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+230)
   (* i c)
   (if (<= (* c i) -5e+164) (* b a) (if (<= (* c i) 1e+78) (* t z) (* 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) <= -1e+230) {
		tmp = i * c;
	} else if ((c * i) <= -5e+164) {
		tmp = b * a;
	} else if ((c * i) <= 1e+78) {
		tmp = t * z;
	} 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) <= (-1d+230)) then
        tmp = i * c
    else if ((c * i) <= (-5d+164)) then
        tmp = b * a
    else if ((c * i) <= 1d+78) then
        tmp = t * z
    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) <= -1e+230) {
		tmp = i * c;
	} else if ((c * i) <= -5e+164) {
		tmp = b * a;
	} else if ((c * i) <= 1e+78) {
		tmp = t * z;
	} else {
		tmp = i * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+230:
		tmp = i * c
	elif (c * i) <= -5e+164:
		tmp = b * a
	elif (c * i) <= 1e+78:
		tmp = t * z
	else:
		tmp = i * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+230)
		tmp = Float64(i * c);
	elseif (Float64(c * i) <= -5e+164)
		tmp = Float64(b * a);
	elseif (Float64(c * i) <= 1e+78)
		tmp = Float64(t * z);
	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) <= -1e+230)
		tmp = i * c;
	elseif ((c * i) <= -5e+164)
		tmp = b * a;
	elseif ((c * i) <= 1e+78)
		tmp = t * z;
	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], -1e+230], N[(i * c), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5e+164], N[(b * a), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+78], N[(t * z), $MachinePrecision], N[(i * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.0000000000000001e230 or 1.00000000000000001e78 < (*.f64 c i)

   1. Initial program 90.2%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 72.9

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

   5. Applied rewrites 72.9%

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

   if -1.0000000000000001e230 < (*.f64 c i) < -4.9999999999999995e164

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

   if -4.9999999999999995e164 < (*.f64 c i) < 1.00000000000000001e78

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 42.8

         \[\leadsto t \cdot \color{blue}{z} \]

   5. Applied rewrites 42.8%

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

Alternative 9: 62.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+228} \lor \neg \left(c \cdot i \leq 10^{+139}\right):\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1e+228) (not (<= (* c i) 1e+139)))
   (* i c)
   (fma t z (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1e+228) || !((c * i) <= 1e+139)) {
		tmp = i * c;
	} else {
		tmp = fma(t, z, (y * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1e+228) || !(Float64(c * i) <= 1e+139))
		tmp = Float64(i * c);
	else
		tmp = fma(t, z, Float64(y * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1e+228], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1e+139]], $MachinePrecision]], N[(i * c), $MachinePrecision], N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.9999999999999992e227 or 1.00000000000000003e139 < (*.f64 c i)

   1. Initial program 88.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if -9.9999999999999992e227 < (*.f64 c i) < 1.00000000000000003e139

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{c \cdot i + \left(t \cdot z + x \cdot y\right)} \]
   4. 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 76.4

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 68.8

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

   8. Applied rewrites 68.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+228} \lor \neg \left(c \cdot i \leq 10^{+139}\right):\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230} \lor \neg \left(c \cdot i \leq 10^{+78}\right):\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1e+230) (not (<= (* c i) 1e+78))) (* 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) <= -1e+230) || !((c * i) <= 1e+78)) {
		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) <= (-1d+230)) .or. (.not. ((c * i) <= 1d+78))) 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) <= -1e+230) || !((c * i) <= 1e+78)) {
		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) <= -1e+230) or not ((c * i) <= 1e+78):
		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) <= -1e+230) || !(Float64(c * i) <= 1e+78))
		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) <= -1e+230) || ~(((c * i) <= 1e+78)))
		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], -1e+230], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1e+78]], $MachinePrecision]], N[(i * c), $MachinePrecision], N[(b * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.0000000000000001e230 or 1.00000000000000001e78 < (*.f64 c i)

   1. Initial program 90.2%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 72.9

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

   5. Applied rewrites 72.9%

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

   if -1.0000000000000001e230 < (*.f64 c i) < 1.00000000000000001e78

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 27.0

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

   5. Applied rewrites 27.0%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+230} \lor \neg \left(c \cdot i \leq 10^{+78}\right):\\ \;\;\;\;i \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.0% 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 95.3%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 22.9

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

5. Applied rewrites 22.9%

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

Reproduce

herbie shell --seed 2025043 
(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)))