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

Percentage Accurate: 100.0% → 100.0%

Time: 1.6s

Precision: binary64

Cost: 6784

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[0.5 \cdot \left(x \cdot x - y\right) \]

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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. Applied egg-rr 100.0%

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

   [Start] 100.0%	\[ 0.5 \cdot \left(x \cdot x - y\right) \]
   fma-neg [=>] 100.0%	\[ 0.5 \cdot \color{blue}{\mathsf{fma}\left(x, x, -y\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	6784

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

Alternative 2
Accuracy	86.5%
Cost	580

\[\begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.2 \cdot 10^{+66}:\\ \;\;\;\;0.5 \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 3
Accuracy	100.0%
Cost	448

\[0.5 \cdot \left(x \cdot x - y\right) \]

Alternative 4
Accuracy	50.1%
Cost	256

\[0.5 \cdot \left(-y\right) \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))