fma_test2

Percentage Accurate: 33.8% → 99.6%

Time: 2.2s

Alternatives: 4

Speedup: 1.6×

Specification

\[1.9 \leq t \land t \leq 2.1\]

Math

\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

FPCore

(FPCore (t)
  :precision binary64
  (- (* 1.7e+308 t) 1.7e+308))

C

double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

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 = (1.7d+308 * t) - 1.7d+308
end function

Java

public static double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

Python

def code(t):
	return (1.7e+308 * t) - 1.7e+308

Julia

function code(t)
	return Float64(Float64(1.7e+308 * t) - 1.7e+308)
end

MATLAB

function tmp = code(t)
	tmp = (1.7e+308 * t) - 1.7e+308;
end

Wolfram

code[t_] := N[(N[(1.7e+308 * t), $MachinePrecision] - 1.7e+308), $MachinePrecision]

Initial Program: 33.8% accurate, 1.0× speedup

Math

\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

FPCore

(FPCore (t)
  :precision binary64
  (- (* 1.7e+308 t) 1.7e+308))

C

double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

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 = (1.7d+308 * t) - 1.7d+308
end function

Java

public static double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

Python

def code(t):
	return (1.7e+308 * t) - 1.7e+308

Julia

function code(t)
	return Float64(Float64(1.7e+308 * t) - 1.7e+308)
end

MATLAB

function tmp = code(t)
	tmp = (1.7e+308 * t) - 1.7e+308;
end

Wolfram

code[t_] := N[(N[(1.7e+308 * t), $MachinePrecision] - 1.7e+308), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.6× speedup

Math

\[\left(1.7 \cdot 10^{+308} - \frac{1.7 \cdot 10^{+308}}{t}\right) \cdot t \]

FPCore

(FPCore (t)
  :precision binary64
  (* (- 1.7e+308 (/ 1.7e+308 t)) t))

C

double code(double t) {
	return (1.7e+308 - (1.7e+308 / t)) * 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 = (1.7d+308 - (1.7d+308 / t)) * t
end function

Java

public static double code(double t) {
	return (1.7e+308 - (1.7e+308 / t)) * t;
}

Python

def code(t):
	return (1.7e+308 - (1.7e+308 / t)) * t

Julia

function code(t)
	return Float64(Float64(1.7e+308 - Float64(1.7e+308 / t)) * t)
end

MATLAB

function tmp = code(t)
	tmp = (1.7e+308 - (1.7e+308 / t)) * t;
end

Wolfram

code[t_] := N[(N[(1.7e+308 - N[(1.7e+308 / t), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]

Derivation

1. Initial program 33.8%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

2. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto t \cdot \color{blue}{\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right)} \]

   2. lower--.f64 N/A

      \[\leadsto t \cdot \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto t \cdot \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \color{blue}{\frac{1}{t}}\right) \]

   4. lower-/.f64 99.3%

      \[\leadsto t \cdot \left(1.7 \cdot 10^{+308} - 1.7 \cdot 10^{+308} \cdot \frac{1}{\color{blue}{t}}\right) \]

4. Applied rewrites 99.3%

   \[\leadsto \color{blue}{t \cdot \left(1.7 \cdot 10^{+308} - 1.7 \cdot 10^{+308} \cdot \frac{1}{t}\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto t \cdot \color{blue}{\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right) \cdot \color{blue}{t} \]

   3. lower-*.f64 99.3%

      \[\leadsto \left(1.7 \cdot 10^{+308} - 1.7 \cdot 10^{+308} \cdot \frac{1}{t}\right) \cdot \color{blue}{t} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right) \cdot t \]

   5. lift-/.f64 N/A

      \[\leadsto \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right) \cdot t \]

   6. mult-flip-rev N/A

      \[\leadsto \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - \frac{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{t}\right) \cdot t \]

   7. lower-/.f64 99.5%

      \[\leadsto \left(1.7 \cdot 10^{+308} - \frac{1.7 \cdot 10^{+308}}{t}\right) \cdot t \]

6. Applied rewrites 99.5%

   \[\leadsto \left(1.7 \cdot 10^{+308} - \frac{1.7 \cdot 10^{+308}}{t}\right) \cdot \color{blue}{t} \]
7. Add Preprocessing

Alternative 2: 99.5% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, -1.7 \cdot 10^{+308}\right) \]

FPCore

(FPCore (t)
  :precision binary64
  (fma t 1.7e+308 -1.7e+308))

C

double code(double t) {
	return fma(t, 1.7e+308, -1.7e+308);
}

Julia

function code(t)
	return fma(t, 1.7e+308, -1.7e+308)
end

Wolfram

code[t_] := N[(t * 1.7e+308 + -1.7e+308), $MachinePrecision]

Derivation

1. Initial program 33.8%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
2. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]

   2. sub-negate-rev N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t\right)\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \mathsf{neg}\left(\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t}\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{neg}\left(\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - \color{blue}{t \cdot 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\right)\right) \]

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

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + \left(\mathsf{neg}\left(t\right)\right) \cdot 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)}\right) \]

   6. distribute-rgt1-in N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + 1\right) \cdot 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\right) \]

   7. distribute-rgt-neg-in N/A

      \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + 1\right) \cdot \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} \]

   8. distribute-lft1-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) + \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} \]

   9. distribute-lft-neg-out N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)\right)\right)} + \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \]

   10. distribute-rgt-neg-out N/A

       \[\leadsto \color{blue}{t \cdot \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)\right)\right)} + \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \]

   11. remove-double-neg N/A

       \[\leadsto t \cdot \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} + \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \]

   12. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(t, 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, \mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} \]

   13. metadata-eval 99.6%

       \[\leadsto \mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, \color{blue}{-1.7 \cdot 10^{+308}}\right) \]

3. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, -1.7 \cdot 10^{+308}\right)} \]
4. Add Preprocessing

Alternative 3: 33.8% accurate, 1.6× speedup

Math

\[t \cdot 1.7 \cdot 10^{+308} \]

FPCore

(FPCore (t)
  :precision binary64
  (* t 1.7e+308))

C

double code(double t) {
	return t * 1.7e+308;
}

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 = t * 1.7d+308
end function

Java

public static double code(double t) {
	return t * 1.7e+308;
}

Python

def code(t):
	return t * 1.7e+308

Julia

function code(t)
	return Float64(t * 1.7e+308)
end

MATLAB

function tmp = code(t)
	tmp = t * 1.7e+308;
end

Wolfram

code[t_] := N[(t * 1.7e+308), $MachinePrecision]

Derivation

1. Initial program 33.8%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

2. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto t \cdot \color{blue}{\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}\right)} \]

   2. lower--.f64 N/A

      \[\leadsto t \cdot \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \frac{1}{t}}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto t \cdot \left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot \color{blue}{\frac{1}{t}}\right) \]

   4. lower-/.f64 99.3%

      \[\leadsto t \cdot \left(1.7 \cdot 10^{+308} - 1.7 \cdot 10^{+308} \cdot \frac{1}{\color{blue}{t}}\right) \]

4. Applied rewrites 99.3%

   \[\leadsto \color{blue}{t \cdot \left(1.7 \cdot 10^{+308} - 1.7 \cdot 10^{+308} \cdot \frac{1}{t}\right)} \]

5. Taylor expanded in t around inf

   \[\leadsto t \cdot 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \]
6. Step-by-step derivation

7. Applied rewrites 33.8%

   \[\leadsto t \cdot 1.7 \cdot 10^{+308} \]
8. Add Preprocessing

Alternative 4: 0.0% accurate, 6.6× speedup

Math

\[-1.7 \cdot 10^{+308} \]

FPCore

(FPCore (t)
  :precision binary64
  -1.7e+308)

C

double code(double t) {
	return -1.7e+308;
}

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 = -1.7d+308
end function

Java

public static double code(double t) {
	return -1.7e+308;
}

Python

def code(t):
	return -1.7e+308

Julia

function code(t)
	return -1.7e+308
end

MATLAB

function tmp = code(t)
	tmp = -1.7e+308;
end

Wolfram

code[t_] := -1.7e+308

Derivation

1. Initial program 33.8%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

2. Taylor expanded in t around 0

   \[\leadsto \color{blue}{-170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]
3. Step-by-step derivation

4. Applied rewrites 0.0%

   \[\leadsto \color{blue}{-1.7 \cdot 10^{+308}} \]
5. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.9× speedup

Math

\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]

FPCore

(FPCore (t)
  :precision binary64
  (fma 1.7e+308 t (- 1.7e+308)))

C

double code(double t) {
	return fma(1.7e+308, t, -1.7e+308);
}

Julia

function code(t)
	return fma(1.7e+308, t, Float64(-1.7e+308))
end

Wolfram

code[t_] := N[(1.7e+308 * t + (-1.7e+308)), $MachinePrecision]

Reproduce

herbie shell --seed 2025233 
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (and (<= 1.9 t) (<= t 2.1))

  :alt
  (! :herbie-platform c (let ((x 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)) (fma x t (- x))))

  (- (* 1.7e+308 t) 1.7e+308))