fma_test1

Percentage Accurate: 3.4% → 99.3%

Time: 2.8s

Alternatives: 5

Speedup: 26.6×

Specification

\[0.9 \leq t \land t \leq 1.1\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + t \cdot 2 \cdot 10^{-16}\\ t\_1 \cdot t\_1 + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (* t 2e-16))))
   (+ (* t_1 t_1) (- -1.0 (* 2.0 (* t 2e-16))))))

C

double code(double t) {
	double t_1 = 1.0 + (t * 2e-16);
	return (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)));
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = 1.0d0 + (t * 2d-16)
    code = (t_1 * t_1) + ((-1.0d0) - (2.0d0 * (t * 2d-16)))
end function

Java

public static double code(double t) {
	double t_1 = 1.0 + (t * 2e-16);
	return (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)));
}

Python

def code(t):
	t_1 = 1.0 + (t * 2e-16)
	return (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)))

Julia

function code(t)
	t_1 = Float64(1.0 + Float64(t * 2e-16))
	return Float64(Float64(t_1 * t_1) + Float64(-1.0 - Float64(2.0 * Float64(t * 2e-16))))
end

MATLAB

function tmp = code(t)
	t_1 = 1.0 + (t * 2e-16);
	tmp = (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)));
end

Wolfram

code[t_] := Block[{t$95$1 = N[(1.0 + N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$1 * t$95$1), $MachinePrecision] + N[(-1.0 - N[(2.0 * N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Initial Program: 3.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + t \cdot 2 \cdot 10^{-16}\\ t\_1 \cdot t\_1 + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (* t 2e-16))))
   (+ (* t_1 t_1) (- -1.0 (* 2.0 (* t 2e-16))))))

C

double code(double t) {
	double t_1 = 1.0 + (t * 2e-16);
	return (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)));
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = 1.0d0 + (t * 2d-16)
    code = (t_1 * t_1) + ((-1.0d0) - (2.0d0 * (t * 2d-16)))
end function

Java

public static double code(double t) {
	double t_1 = 1.0 + (t * 2e-16);
	return (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)));
}

Python

def code(t):
	t_1 = 1.0 + (t * 2e-16)
	return (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)))

Julia

function code(t)
	t_1 = Float64(1.0 + Float64(t * 2e-16))
	return Float64(Float64(t_1 * t_1) + Float64(-1.0 - Float64(2.0 * Float64(t * 2e-16))))
end

MATLAB

function tmp = code(t)
	t_1 = 1.0 + (t * 2e-16);
	tmp = (t_1 * t_1) + (-1.0 - (2.0 * (t * 2e-16)));
end

Wolfram

code[t_] := Block[{t$95$1 = N[(1.0 + N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]}, N[(N[(t$95$1 * t$95$1), $MachinePrecision] + N[(-1.0 - N[(2.0 * N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 99.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ 4 \cdot 10^{-32} \cdot {t}^{2} \end{array} \]

FPCore

(FPCore (t) :precision binary64 (* 4e-32 (pow t 2.0)))

C

double code(double t) {
	return 4e-32 * pow(t, 2.0);
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    code = 4d-32 * (t ** 2.0d0)
end function

Java

public static double code(double t) {
	return 4e-32 * Math.pow(t, 2.0);
}

Python

def code(t):
	return 4e-32 * math.pow(t, 2.0)

Julia

function code(t)
	return Float64(4e-32 * (t ^ 2.0))
end

MATLAB

function tmp = code(t)
	tmp = 4e-32 * (t ^ 2.0);
end

Wolfram

code[t_] := N[(4e-32 * N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 3.4%

   \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \]

2. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{1}{25000000000000000000000000000000} \cdot {t}^{2}} \]

4. Applied rewrites 99.3%

   \[\leadsto \color{blue}{4 \cdot 10^{-32} \cdot {t}^{2}} \]
5. Add Preprocessing

Alternative 2: 25.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot 10^{-16} \cdot 2 \cdot 10^{-16}\right) \cdot t \end{array} \]

FPCore

(FPCore (t) :precision binary64 (* (* 2e-16 2e-16) t))

C

double code(double t) {
	return (2e-16 * 2e-16) * t;
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    code = (2d-16 * 2d-16) * t
end function

Java

public static double code(double t) {
	return (2e-16 * 2e-16) * t;
}

Python

def code(t):
	return (2e-16 * 2e-16) * t

Julia

function code(t)
	return Float64(Float64(2e-16 * 2e-16) * t)
end

MATLAB

function tmp = code(t)
	tmp = (2e-16 * 2e-16) * t;
end

Wolfram

code[t_] := N[(N[(2e-16 * 2e-16), $MachinePrecision] * t), $MachinePrecision]

Derivation

1. Initial program 3.4%

   \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \]

3. Applied rewrites 8.3%

   \[\leadsto \color{blue}{1} \]

5. Applied rewrites 9.8%

   \[\leadsto \color{blue}{2 \cdot 10^{-16}} \]

7. Applied rewrites 25.1%

   \[\leadsto \color{blue}{\left(2 \cdot 10^{-16} \cdot 2 \cdot 10^{-16}\right) \cdot t} \]
8. Add Preprocessing

Alternative 3: 25.1% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ 4 \cdot 10^{-32} \cdot t \end{array} \]

FPCore

(FPCore (t) :precision binary64 (* 4e-32 t))

C

double code(double t) {
	return 4e-32 * t;
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    code = 4d-32 * t
end function

Java

public static double code(double t) {
	return 4e-32 * t;
}

Python

def code(t):
	return 4e-32 * t

Julia

function code(t)
	return Float64(4e-32 * t)
end

MATLAB

function tmp = code(t)
	tmp = 4e-32 * t;
end

Wolfram

code[t_] := N[(4e-32 * t), $MachinePrecision]

Derivation

1. Initial program 3.4%

   \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \]

3. Applied rewrites 8.3%

   \[\leadsto \color{blue}{1} \]

5. Applied rewrites 9.8%

   \[\leadsto \color{blue}{2 \cdot 10^{-16}} \]

7. Applied rewrites 25.1%

   \[\leadsto \color{blue}{\left(2 \cdot 10^{-16} \cdot 2 \cdot 10^{-16}\right) \cdot t} \]

8. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{1}{25000000000000000000000000000000} \cdot t} \]

10. Applied rewrites 25.1%

    \[\leadsto \color{blue}{4 \cdot 10^{-32} \cdot t} \]
11. Add Preprocessing

Alternative 4: 23.6% accurate, 26.6× speedup

Math

\[\begin{array}{l} \\ 4 \cdot 10^{-32} \end{array} \]

FPCore

(FPCore (t) :precision binary64 4e-32)

C

double code(double t) {
	return 4e-32;
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    code = 4d-32
end function

Java

public static double code(double t) {
	return 4e-32;
}

Python

def code(t):
	return 4e-32

Julia

function code(t)
	return 4e-32
end

MATLAB

function tmp = code(t)
	tmp = 4e-32;
end

Wolfram

code[t_] := 4e-32

Derivation

1. Initial program 3.4%

   \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \]

2. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{1}{25000000000000000000000000000000} \cdot {t}^{2}} \]

4. Applied rewrites 99.3%

   \[\leadsto \color{blue}{4 \cdot 10^{-32} \cdot {t}^{2}} \]

6. Applied rewrites 23.6%

   \[\leadsto 1 \cdot \color{blue}{4 \cdot 10^{-32}} \]

8. Applied rewrites 23.6%

   \[\leadsto 4 \cdot 10^{-32} \]
9. Add Preprocessing

Alternative 5: 9.8% accurate, 26.6× speedup

Math

\[\begin{array}{l} \\ 2 \cdot 10^{-16} \end{array} \]

FPCore

(FPCore (t) :precision binary64 2e-16)

C

double code(double t) {
	return 2e-16;
}

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(t)
use fmin_fmax_functions
    real(8), intent (in) :: t
    code = 2d-16
end function

Java

public static double code(double t) {
	return 2e-16;
}

Python

def code(t):
	return 2e-16

Julia

function code(t)
	return 2e-16
end

MATLAB

function tmp = code(t)
	tmp = 2e-16;
end

Wolfram

code[t_] := 2e-16

Derivation

1. Initial program 3.4%

   \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \]

3. Applied rewrites 8.3%

   \[\leadsto \color{blue}{1} \]

5. Applied rewrites 9.8%

   \[\leadsto \color{blue}{2 \cdot 10^{-16}} \]
6. Add Preprocessing

Developer Target 1: 21.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + t \cdot 2 \cdot 10^{-16}\\ \mathsf{fma}\left(t\_1, t\_1, -1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right) \end{array} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (* t 2e-16)))) (fma t_1 t_1 (- -1.0 (* 2.0 (* t 2e-16))))))

C

double code(double t) {
	double t_1 = 1.0 + (t * 2e-16);
	return fma(t_1, t_1, (-1.0 - (2.0 * (t * 2e-16))));
}

Julia

function code(t)
	t_1 = Float64(1.0 + Float64(t * 2e-16))
	return fma(t_1, t_1, Float64(-1.0 - Float64(2.0 * Float64(t * 2e-16))))
end

Wolfram

code[t_] := Block[{t$95$1 = N[(1.0 + N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]}, N[(t$95$1 * t$95$1 + N[(-1.0 - N[(2.0 * N[(t * 2e-16), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2025159 
(FPCore (t)
  :name "fma_test1"
  :precision binary64
  :pre (and (<= 0.9 t) (<= t 1.1))

  :alt
  (! :herbie-platform c (let ((x (+ 1 (* t 1/5000000000000000))) (z (- -1 (* 2 (* t 1/5000000000000000))))) (fma x x z)))

  (+ (* (+ 1.0 (* t 2e-16)) (+ 1.0 (* t 2e-16))) (- -1.0 (* 2.0 (* t 2e-16)))))