?

Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
Cost: 6976

?

\[\left(5 \leq a \land a \leq 10\right) \land \left(0 \leq b \land b \leq 0.001\right)\]
\[ \begin{array}{c}[a, b] = \mathsf{sort}([a, b])\\ \end{array} \]
\[\left(a + b\right) \cdot \left(a + b\right) \]
↓
\[\mathsf{fma}\left(b + a, b, a \cdot \left(b + a\right)\right) \]
(FPCore (a b) :precision binary64 (* (+ a b) (+ a b)))
↓
(FPCore (a b) :precision binary64 (fma (+ b a) b (* a (+ b a))))
double code(double a, double b) {
	return (a + b) * (a + b);
}
↓
double code(double a, double b) {
	return fma((b + a), b, (a * (b + a)));
}

function code(a, b)
	return Float64(Float64(a + b) * Float64(a + b))
end
↓
function code(a, b)
	return fma(Float64(b + a), b, Float64(a * Float64(b + a)))
end

code[a_, b_] := N[(N[(a + b), $MachinePrecision] * N[(a + b), $MachinePrecision]), $MachinePrecision]
↓
code[a_, b_] := N[(N[(b + a), $MachinePrecision] * b + N[(a * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(a + b\right) \cdot \left(a + b\right)
↓
\mathsf{fma}\left(b + a, b, a \cdot \left(b + a\right)\right)

Error?

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a \]

Derivation?

  1. Initial program 0.0

    \[\left(a + b\right) \cdot \left(a + b\right) \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{b \cdot \left(a + b\right) + a \cdot \left(a + b\right)} \]

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(b + a, b, a \cdot \left(b + a\right)\right)} \]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(b + a, b, a \cdot \left(b + a\right)\right) \]

Alternatives

Alternative 1
Error0.0
Cost704
\[b \cdot \left(b + a\right) + a \cdot \left(b + a\right) \]
Alternative 2
Error0.1
Cost448
\[b \cdot \left(b + a \cdot 2\right) \]
Alternative 3
Error0.0
Cost448
\[\left(b + a\right) \cdot \left(b + a\right) \]
Alternative 4
Error0.7
Cost192
\[b \cdot b \]

Error

Reproduce?

herbie shell --seed 2023073 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (and (<= 5.0 a) (<= a 10.0)) (and (<= 0.0 b) (<= b 0.001)))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))