Average Error: 0.0 → 0
Time: 1.3s
Precision: binary64
\[0 \leq x \land x \leq 2\]
\[x + x \cdot x \]
↓
\[\mathsf{fma}\left(x, x, x\right) \]
(FPCore (x) :precision binary64 (+ x (* x x)))
↓
(FPCore (x) :precision binary64 (fma x x x))
double code(double x) {
	return x + (x * x);
}
↓
double code(double x) {
	return fma(x, x, x);
}

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

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

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

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0
\[\left(1 + x\right) \cdot x \]

Derivation

  1. Initial program 0.0

    \[x + x \cdot x \]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2022180 
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 2.0))

  :herbie-target
  (* (+ 1.0 x) x)

  (+ x (* x x)))