fabs fraction 2

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 3

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ \frac{\left|a - b\right|}{2} \end{array} \]

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)
    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

\[\begin{array}{l} \\ \frac{\left|a - b\right|}{2} \end{array} \]

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)
    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, 1.5× speedup

Math

\[\begin{array}{l} \\ \left|a - b\right| \cdot 0.5 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. div-inv N/A

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

   2. *-lowering-*.f64 N/A

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

   3. fabs-lowering-fabs.f64 N/A

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

   4. --lowering--.f64 N/A

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

   5. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 61.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-116}:\\ \;\;\;\;0.5 \cdot \left|a\right|\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left|b\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 3.4e-116) (* 0.5 (fabs a)) (* 0.5 (fabs b))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 3.4e-116) {
		tmp = 0.5 * fabs(a);
	} else {
		tmp = 0.5 * fabs(b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.4d-116) then
        tmp = 0.5d0 * abs(a)
    else
        tmp = 0.5d0 * abs(b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 3.4e-116) {
		tmp = 0.5 * Math.abs(a);
	} else {
		tmp = 0.5 * Math.abs(b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 3.4e-116:
		tmp = 0.5 * math.fabs(a)
	else:
		tmp = 0.5 * math.fabs(b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 3.4e-116)
		tmp = Float64(0.5 * abs(a));
	else
		tmp = Float64(0.5 * abs(b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 3.4e-116)
		tmp = 0.5 * abs(a);
	else
		tmp = 0.5 * abs(b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 3.4e-116], N[(0.5 * N[Abs[a], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[Abs[b], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.39999999999999992e-116

   1. Initial program 100.0%

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

      1. div-inv N/A

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

      2. *-lowering-*.f64 N/A

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

      3. fabs-lowering-fabs.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto \left|\color{blue}{a}\right| \cdot \frac{1}{2} \]
   6. Step-by-step derivation

   7. Simplified 54.6%

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

   if 3.39999999999999992e-116 < b

   1. Initial program 100.0%

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

      1. div-inv N/A

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

      2. *-lowering-*.f64 N/A

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

      3. fabs-lowering-fabs.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0

      \[\leadsto \left|\color{blue}{-1 \cdot b}\right| \cdot \frac{1}{2} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left|\color{blue}{\mathsf{neg}\left(b\right)}\right| \cdot \frac{1}{2} \]

      2. neg-lowering-neg.f64 72.5

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

   7. Simplified 72.5%

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

      1. fabs-neg N/A

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

      2. fabs-lowering-fabs.f64 72.5

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

   9. Applied egg-rr 72.5%

      \[\leadsto \color{blue}{\left|b\right|} \cdot 0.5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-116}:\\ \;\;\;\;0.5 \cdot \left|a\right|\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left|b\right|\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left|a\right| \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. div-inv N/A

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

   2. *-lowering-*.f64 N/A

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

   3. fabs-lowering-fabs.f64 N/A

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

   4. --lowering--.f64 N/A

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

   5. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in a around inf

   \[\leadsto \left|\color{blue}{a}\right| \cdot \frac{1}{2} \]
6. Step-by-step derivation

7. Simplified 46.3%

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

8. Final simplification 46.3%

   \[\leadsto 0.5 \cdot \left|a\right| \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024201 
(FPCore (a b)
  :name "fabs fraction 2"
  :precision binary64
  (/ (fabs (- a b)) 2.0))