System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

Percentage Accurate: 100.0% → 100.0%

Time: 11.0s

Alternatives: 4

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(N[(x * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(N[(x * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \mathsf{fma}\left(x, x, -y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (fma x x (- y))))

C

double code(double x, double y) {
	return 0.5 * fma(x, x, -y);
}

Julia

function code(x, y)
	return Float64(0.5 * fma(x, x, Float64(-y)))
end

Wolfram

code[x_, y_] := N[(0.5 * N[(x * x + (-y)), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. fma-neg 100.0%

      \[\leadsto 0.5 \cdot \color{blue}{\mathsf{fma}\left(x, x, -y\right)} \]

4. Applied egg-rr 100.0%

   \[\leadsto 0.5 \cdot \color{blue}{\mathsf{fma}\left(x, x, -y\right)} \]

5. Final simplification 100.0%

   \[\leadsto 0.5 \cdot \mathsf{fma}\left(x, x, -y\right) \]
6. Add Preprocessing

Alternative 2: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))

C

double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * ((x * x) - y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}

Python

def code(x, y):
	return 0.5 * ((x * x) - y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(Float64(x * x) - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * ((x * x) - y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(N[(x * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto 0.5 \cdot \left(x \cdot x - y\right) \]
4. Add Preprocessing

Alternative 3: 51.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ y \cdot -0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y -0.5))

C

double code(double x, double y) {
	return y * -0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (-0.5d0)
end function

Java

public static double code(double x, double y) {
	return y * -0.5;
}

Python

def code(x, y):
	return y * -0.5

Julia

function code(x, y)
	return Float64(y * -0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = y * -0.5;
end

Wolfram

code[x_, y_] := N[(y * -0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 49.9%

   \[\leadsto 0.5 \cdot \color{blue}{\left(-1 \cdot y\right)} \]
4. Step-by-step derivation

   1. neg-mul-1 49.9%

      \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

5. Simplified 49.9%

   \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

6. Taylor expanded in y around 0 49.9%

   \[\leadsto \color{blue}{-0.5 \cdot y} \]
7. Step-by-step derivation

   1. *-commutative 49.9%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

8. Simplified 49.9%

   \[\leadsto \color{blue}{y \cdot -0.5} \]

9. Final simplification 49.9%

   \[\leadsto y \cdot -0.5 \]
10. Add Preprocessing

Alternative 4: 2.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 100.0%

   \[0.5 \cdot \left(x \cdot x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 49.9%

   \[\leadsto 0.5 \cdot \color{blue}{\left(-1 \cdot y\right)} \]
4. Step-by-step derivation

   1. neg-mul-1 49.9%

      \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]

5. Simplified 49.9%

   \[\leadsto 0.5 \cdot \color{blue}{\left(-y\right)} \]
6. Step-by-step derivation

   1. add-log-exp 9.1%

      \[\leadsto 0.5 \cdot \color{blue}{\log \left(e^{-y}\right)} \]

   2. pow1 9.1%

      \[\leadsto 0.5 \cdot \log \color{blue}{\left({\left(e^{-y}\right)}^{1}\right)} \]

   3. metadata-eval 9.1%

      \[\leadsto 0.5 \cdot \log \left({\left(e^{-y}\right)}^{\color{blue}{\left(0.5 + 0.5\right)}}\right) \]

   4. pow-prod-up 9.0%

      \[\leadsto 0.5 \cdot \log \color{blue}{\left({\left(e^{-y}\right)}^{0.5} \cdot {\left(e^{-y}\right)}^{0.5}\right)} \]

   5. exp-prod 9.1%

      \[\leadsto 0.5 \cdot \log \left(\color{blue}{e^{\left(-y\right) \cdot 0.5}} \cdot {\left(e^{-y}\right)}^{0.5}\right) \]

   6. *-commutative 9.1%

      \[\leadsto 0.5 \cdot \log \left(e^{\color{blue}{0.5 \cdot \left(-y\right)}} \cdot {\left(e^{-y}\right)}^{0.5}\right) \]

   7. exp-prod 9.1%

      \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot \color{blue}{e^{\left(-y\right) \cdot 0.5}}\right) \]

   8. *-commutative 9.1%

      \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot e^{\color{blue}{0.5 \cdot \left(-y\right)}}\right) \]

   9. exp-prod 9.1%

      \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot \color{blue}{{\left(e^{0.5}\right)}^{\left(-y\right)}}\right) \]

   10. add-sqr-sqrt 1.7%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot {\left(e^{0.5}\right)}^{\left(-\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right)}\right) \]

   11. sqrt-unprod 2.6%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot {\left(e^{0.5}\right)}^{\left(-\color{blue}{\sqrt{y \cdot y}}\right)}\right) \]

   12. sqr-neg 2.6%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot {\left(e^{0.5}\right)}^{\left(-\sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right)}\right) \]

   13. sqrt-unprod 0.9%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot {\left(e^{0.5}\right)}^{\left(-\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}\right)}\right) \]

   14. add-sqr-sqrt 1.7%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot {\left(e^{0.5}\right)}^{\left(-\color{blue}{\left(-y\right)}\right)}\right) \]

   15. pow-neg 1.7%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot \color{blue}{\frac{1}{{\left(e^{0.5}\right)}^{\left(-y\right)}}}\right) \]

   16. exp-prod 1.7%

       \[\leadsto 0.5 \cdot \log \left(e^{0.5 \cdot \left(-y\right)} \cdot \frac{1}{\color{blue}{e^{0.5 \cdot \left(-y\right)}}}\right) \]

   17. rgt-mult-inverse 2.6%

       \[\leadsto 0.5 \cdot \log \color{blue}{1} \]

   18. metadata-eval 2.6%

       \[\leadsto 0.5 \cdot \color{blue}{0} \]

7. Applied egg-rr 2.6%

   \[\leadsto 0.5 \cdot \color{blue}{0} \]
8. Step-by-step derivation

   1. metadata-eval 2.6%

      \[\leadsto \color{blue}{0} \]

9. Applied egg-rr 2.6%

   \[\leadsto \color{blue}{0} \]

10. Final simplification 2.6%

    \[\leadsto 0 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024068 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))