Average Error: 0.0 → 0
Time: 2.5s
Precision: binary64
Cost: 6720
\[\left(x \cdot x + y\right) + y \]
↓
\[\mathsf{fma}\left(x, x, y + y\right) \]
(FPCore (x y) :precision binary64 (+ (+ (* x x) y) y))
↓
(FPCore (x y) :precision binary64 (fma x x (+ y y)))
double code(double x, double y) {
	return ((x * x) + y) + y;
}
↓
double code(double x, double y) {
	return fma(x, x, (y + y));
}

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

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

\left(x \cdot x + y\right) + y
↓
\mathsf{fma}\left(x, x, y + y\right)

Error

Target

Original0.0
Target0.0
Herbie0
\[\left(y + y\right) + x \cdot x \]

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0

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

  3. Final simplification0

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

Alternatives

Alternative 1
Error9.9
Cost584
\[\begin{array}{l} t_0 := y + x \cdot x\\ \mathbf{if}\;x \leq -54.801187030765554:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4704233692169524 \cdot 10^{-42}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error37.7
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -2.4495616745873813 \cdot 10^{-55}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 3.549486702895513 \cdot 10^{-100}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 3
Error10.9
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -236919.7790335652:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.4704233692169524 \cdot 10^{-42}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[y + \left(y + x \cdot x\right) \]
Alternative 5
Error55.4
Cost64
\[y \]

Error

Reproduce

herbie shell --seed 2022318 
(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))