Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5

Percentage Accurate: 100.0% → 100.0%

Time: 1.6s

Alternatives: 3

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \frac{\left|x - y\right|}{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))

C

double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function

Java

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}

Python

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)

Julia

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end

Wolfram

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left|x - y\right|}{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))

C

double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function

Java

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}

Python

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)

Julia

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end

Wolfram

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \left|\frac{x}{y} + -1\right| \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fabs (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	return fabs(((x / y) + -1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs(((x / y) + (-1.0d0)))
end function

Java

public static double code(double x, double y) {
	return Math.abs(((x / y) + -1.0));
}

Python

def code(x, y):
	return math.fabs(((x / y) + -1.0))

Julia

function code(x, y)
	return abs(Float64(Float64(x / y) + -1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = abs(((x / y) + -1.0));
end

Wolfram

code[x_, y_] := N[Abs[N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. div-fabs 100.0%

      \[\leadsto \color{blue}{\left|\frac{x - y}{y}\right|} \]

   2. div-sub 100.0%

      \[\leadsto \left|\color{blue}{\frac{x}{y} - \frac{y}{y}}\right| \]

   3. pow1 100.0%

      \[\leadsto \left|\frac{x}{y} - \frac{\color{blue}{{y}^{1}}}{y}\right| \]

   4. pow1 100.0%

      \[\leadsto \left|\frac{x}{y} - \frac{{y}^{1}}{\color{blue}{{y}^{1}}}\right| \]

   5. pow-div 100.0%

      \[\leadsto \left|\frac{x}{y} - \color{blue}{{y}^{\left(1 - 1\right)}}\right| \]

   6. metadata-eval 100.0%

      \[\leadsto \left|\frac{x}{y} - {y}^{\color{blue}{0}}\right| \]

   7. metadata-eval 100.0%

      \[\leadsto \left|\frac{x}{y} - \color{blue}{1}\right| \]

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left|\frac{x}{y} - 1\right|} \]

4. Final simplification 100.0%

   \[\leadsto \left|\frac{x}{y} + -1\right| \]

Alternative 2: 26.6% accurate, 68.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x y))

C

double code(double x, double y) {
	return x / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / y
end function

Java

public static double code(double x, double y) {
	return x / y;
}

Python

def code(x, y):
	return x / y

Julia

function code(x, y)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y)
	tmp = x / y;
end

Wolfram

code[x_, y_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. add-sqr-sqrt 46.2%

      \[\leadsto \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{\left|y\right|} \]

   2. fabs-sqr 46.2%

      \[\leadsto \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{\left|y\right|} \]

   3. add-sqr-sqrt 14.0%

      \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \]

   4. fabs-sqr 14.0%

      \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

   5. add-sqr-sqrt 14.5%

      \[\leadsto \frac{\color{blue}{x - y}}{\sqrt{y} \cdot \sqrt{y}} \]

   6. add-sqr-sqrt 26.3%

      \[\leadsto \frac{x - y}{\color{blue}{y}} \]

   7. clear-num 26.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x - y}}} \]

   8. associate-/r/ 26.2%

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

3. Applied egg-rr 26.2%

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

4. Taylor expanded in y around 0 27.0%

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

5. Final simplification 27.0%

   \[\leadsto \frac{x}{y} \]

Alternative 3: 1.3% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

   1. add-sqr-sqrt 46.2%

      \[\leadsto \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{\left|y\right|} \]

   2. fabs-sqr 46.2%

      \[\leadsto \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{\left|y\right|} \]

   3. add-sqr-sqrt 14.0%

      \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \]

   4. fabs-sqr 14.0%

      \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

   5. add-sqr-sqrt 14.5%

      \[\leadsto \frac{\color{blue}{x - y}}{\sqrt{y} \cdot \sqrt{y}} \]

   6. add-sqr-sqrt 26.3%

      \[\leadsto \frac{x - y}{\color{blue}{y}} \]

   7. clear-num 26.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x - y}}} \]

   8. associate-/r/ 26.2%

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

3. Applied egg-rr 26.2%

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

4. Taylor expanded in y around inf 1.3%

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

5. Final simplification 1.3%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023340 
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))