Average Error: 0.0 → 0.0
Time: 2.6s
Precision: binary64
Cost: 6720
\[\left(x \cdot x + y\right) + y \]
↓
\[\mathsf{fma}\left(x, x, y\right) + y \]
(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 Float64(fma(x, x, y) + y)
end

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

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

Error

Target

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

Alternatives

Alternative 1
Error10.1
Cost584
\[\begin{array}{l} t_0 := x \cdot x + y\\ \mathbf{if}\;x \leq -30:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 280000000:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error38.0
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-114}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 3
Error11.0
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -5.6:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 7500000000:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[\left(x \cdot x + y\right) + y \]
Alternative 5
Error55.2
Cost64
\[y \]

Error

Reproduce

herbie shell --seed 2023010 
(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))