Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

Average Error: 0.0 → 0

Time: 20.0s

Precision: binary64

Cost: 6720

Math

\[\left(x \cdot x + y\right) + y \]

↓

\[\mathsf{fma}\left(x, x, y + y\right) \]

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x x) y) y))

↓

(FPCore (x y) :precision binary64 (fma x x (+ y y)))

C

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

↓

double code(double x, double y) {
	return fma(x, x, (y + y));
}

Julia

function code(x, y)
	return Float64(Float64(Float64(x * x) + y) + y)
end

↓

function code(x, y)
	return fma(x, x, Float64(y + y))
end

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0

\[\left(y + y\right) + x \cdot x \]

Derivation

1. Initial program 0.0

   \[\left(x \cdot x + y\right) + y \]

2. Applied egg-rr 0

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

Alternatives

Alternative 1
Error	0.0
Cost	6720

\[\mathsf{fma}\left(x, x, y\right) + y \]

Alternative 2
Error	11.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -460:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-48}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

\[\left(x \cdot x + y\right) + y \]

Alternative 4
Error	41.7
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (+ y y) (* x x))

  (+ (+ (* x x) y) y))