fabs fraction 2

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 2

Speedup: 1.1×

Specification

Math

\[\frac{\left|a - b\right|}{2} \]

FPCore

(FPCore (a b)
  :precision binary64
  (/ (fabs (- a b)) 2.0))

C

double code(double a, double b) {
	return fabs((a - b)) / 2.0;
}

Fortran

real(8) function code(a, b)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = abs((a - b)) / 2.0d0
end function

Java

public static double code(double a, double b) {
	return Math.abs((a - b)) / 2.0;
}

Python

def code(a, b):
	return math.fabs((a - b)) / 2.0

Julia

function code(a, b)
	return Float64(abs(Float64(a - b)) / 2.0)
end

MATLAB

function tmp = code(a, b)
	tmp = abs((a - b)) / 2.0;
end

Wolfram

code[a_, b_] := N[(N[Abs[N[(a - b), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{\left|a - b\right|}{2} \]

FPCore

(FPCore (a b)
  :precision binary64
  (/ (fabs (- a b)) 2.0))

C

double code(double a, double b) {
	return fabs((a - b)) / 2.0;
}

Fortran

real(8) function code(a, b)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = abs((a - b)) / 2.0d0
end function

Java

public static double code(double a, double b) {
	return Math.abs((a - b)) / 2.0;
}

Python

def code(a, b):
	return math.fabs((a - b)) / 2.0

Julia

function code(a, b)
	return Float64(abs(Float64(a - b)) / 2.0)
end

MATLAB

function tmp = code(a, b)
	tmp = abs((a - b)) / 2.0;
end

Wolfram

code[a_, b_] := N[(N[Abs[N[(a - b), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\left|b - a\right| \cdot 0.5 \]

FPCore

(FPCore (a b)
  :precision binary64
  (* (fabs (- b a)) 0.5))

C

double code(double a, double b) {
	return fabs((b - a)) * 0.5;
}

Fortran

real(8) function code(a, b)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = abs((b - a)) * 0.5d0
end function

Java

public static double code(double a, double b) {
	return Math.abs((b - a)) * 0.5;
}

Python

def code(a, b):
	return math.fabs((b - a)) * 0.5

Julia

function code(a, b)
	return Float64(abs(Float64(b - a)) * 0.5)
end

MATLAB

function tmp = code(a, b)
	tmp = abs((b - a)) * 0.5;
end

Wolfram

code[a_, b_] := N[(N[Abs[N[(b - a), $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left|a - b\right|}{2} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left|a - b\right|}{2}} \]

   2. mult-flip N/A

      \[\leadsto \color{blue}{\left|a - b\right| \cdot \frac{1}{2}} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left|a - b\right| \cdot \frac{1}{2}} \]

   4. lift-fabs.f64 N/A

      \[\leadsto \color{blue}{\left|a - b\right|} \cdot \frac{1}{2} \]

   5. lift--.f64 N/A

      \[\leadsto \left|\color{blue}{a - b}\right| \cdot \frac{1}{2} \]

   6. fabs-sub N/A

      \[\leadsto \color{blue}{\left|b - a\right|} \cdot \frac{1}{2} \]

   7. lower-fabs.f64 N/A

      \[\leadsto \color{blue}{\left|b - a\right|} \cdot \frac{1}{2} \]

   8. lower--.f64 N/A

      \[\leadsto \left|\color{blue}{b - a}\right| \cdot \frac{1}{2} \]

   9. metadata-eval 100.0%

      \[\leadsto \left|b - a\right| \cdot \color{blue}{0.5} \]

3. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\left|b - a\right| \cdot 0.5} \]
4. Add Preprocessing

Alternative 2: 51.0% accurate, 1.0× speedup

Math

\[\left|\mathsf{max}\left(a, b\right)\right| \cdot 0.5 \]

FPCore

(FPCore (a b)
  :precision binary64
  (* (fabs (fmax a b)) 0.5))

C

double code(double a, double b) {
	return fabs(fmax(a, b)) * 0.5;
}

Fortran

real(8) function code(a, b)
use fmin_fmax_functions
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = abs(fmax(a, b)) * 0.5d0
end function

Java

public static double code(double a, double b) {
	return Math.abs(fmax(a, b)) * 0.5;
}

Python

def code(a, b):
	return math.fabs(fmax(a, b)) * 0.5

Julia

function code(a, b)
	return Float64(abs(fmax(a, b)) * 0.5)
end

MATLAB

function tmp = code(a, b)
	tmp = abs(max(a, b)) * 0.5;
end

Wolfram

code[a_, b_] := N[(N[Abs[N[Max[a, b], $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left|a - b\right|}{2} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left|a - b\right|}{2}} \]

   2. mult-flip N/A

      \[\leadsto \color{blue}{\left|a - b\right| \cdot \frac{1}{2}} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left|a - b\right| \cdot \frac{1}{2}} \]

   4. lift-fabs.f64 N/A

      \[\leadsto \color{blue}{\left|a - b\right|} \cdot \frac{1}{2} \]

   5. lift--.f64 N/A

      \[\leadsto \left|\color{blue}{a - b}\right| \cdot \frac{1}{2} \]

   6. fabs-sub N/A

      \[\leadsto \color{blue}{\left|b - a\right|} \cdot \frac{1}{2} \]

   7. lower-fabs.f64 N/A

      \[\leadsto \color{blue}{\left|b - a\right|} \cdot \frac{1}{2} \]

   8. lower--.f64 N/A

      \[\leadsto \left|\color{blue}{b - a}\right| \cdot \frac{1}{2} \]

   9. metadata-eval 100.0%

      \[\leadsto \left|b - a\right| \cdot \color{blue}{0.5} \]

3. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\left|b - a\right| \cdot 0.5} \]

4. Taylor expanded in a around 0

   \[\leadsto \left|\color{blue}{b}\right| \cdot 0.5 \]
5. Step-by-step derivation

6. Applied rewrites 51.4%

   \[\leadsto \left|\color{blue}{b}\right| \cdot 0.5 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025326 
(FPCore (a b)
  :name "fabs fraction 2"
  :precision binary64
  (/ (fabs (- a b)) 2.0))