Average Error: 0.0 → 0.0
Time: 4.5s
Precision: binary64
Cost: 6976
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]
↓
\[\mathsf{fma}\left(x, x, x \cdot 2\right) + y \cdot y \]
(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (fma x x (* x 2.0)) (* y y)))
double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}
↓
double code(double x, double y) {
	return fma(x, x, (x * 2.0)) + (y * y);
}

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) + Float64(x * x)) + Float64(y * y))
end
↓
function code(x, y)
	return Float64(fma(x, x, Float64(x * 2.0)) + Float64(y * y))
end

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(x * x + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]

\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
\mathsf{fma}\left(x, x, x \cdot 2\right) + y \cdot y

Error

Target

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right) \]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x \cdot 2\right)} + y \cdot y \]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, x \cdot 2\right) + y \cdot y \]

Alternatives

Alternative 1
Error22.2
Cost720
\[\begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-138}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 2
Error4.1
Cost713
\[\begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-14} \lor \neg \left(x \leq 0.39\right):\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \end{array} \]
Alternative 3
Error1.2
Cost713
\[\begin{array}{l} \mathbf{if}\;x \leq -190 \lor \neg \left(x \leq 0.0037\right):\\ \;\;\;\;y \cdot y + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \end{array} \]
Alternative 4
Error4.1
Cost712
\[\begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot x + x \cdot 2\\ \mathbf{elif}\;x \leq 0.225:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \end{array} \]
Alternative 5
Error0.0
Cost704
\[y \cdot y + \left(x \cdot x + x \cdot 2\right) \]
Alternative 6
Error9.7
Cost584
\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 7
Error0.0
Cost576
\[y \cdot y + x \cdot \left(x + 2\right) \]
Alternative 8
Error25.0
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -44000:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 32000000000:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 9
Error45.0
Cost192
\[x \cdot x \]

Error

Reproduce

herbie shell --seed 2022364 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))