Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
Cost: 6848
\[2 \cdot \left(x \cdot x + x \cdot y\right) \]
↓
\[2 \cdot \mathsf{fma}\left(x, x, x \cdot y\right) \]
(FPCore (x y) :precision binary64 (* 2.0 (+ (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* 2.0 (fma x x (* x y))))
double code(double x, double y) {
	return 2.0 * ((x * x) + (x * y));
}
↓
double code(double x, double y) {
	return 2.0 * fma(x, x, (x * y));
}

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

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

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

Error

Target

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

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error9.0
Cost848
\[\begin{array}{l} t_0 := 2 \cdot \left(x \cdot y\right)\\ t_1 := 2 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;y \leq -1.453638413965964 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -23649020298467.67:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3833745838419967 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.232376549514604 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error0.0
Cost576
\[2 \cdot \left(x \cdot y + x \cdot x\right) \]
Alternative 3
Error0.0
Cost448
\[2 \cdot \left(x \cdot \left(x + y\right)\right) \]
Alternative 4
Error22.4
Cost320
\[2 \cdot \left(x \cdot y\right) \]

Error

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

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

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