Average Error: 0.2 → 0.2
Time: 1.4s
Precision: binary64
\[\left(x \cdot 3\right) \cdot x\]
↓
\[3 \cdot {x}^{2}\]
\left(x \cdot 3\right) \cdot x
↓
3 \cdot {x}^{2}
(FPCore (x) :precision binary64 (* (* x 3.0) x))
↓
(FPCore (x) :precision binary64 (* 3.0 (pow x 2.0)))
double code(double x) {
	return (x * 3.0) * x;
}
↓
double code(double x) {
	return 3.0 * pow(x, 2.0);
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(x \cdot 3\right) \cdot x\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{3 \cdot {x}^{2}}\]

  3. Final simplification0.2

    \[\leadsto 3 \cdot {x}^{2}\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))