Average Error: 0.2 → 0.2
Time: 1.1s
Precision: binary64
\[\left(x \cdot 3\right) \cdot x \]
↓
\[x \cdot \left(3 \cdot x\right) \]
\left(x \cdot 3\right) \cdot x
↓
x \cdot \left(3 \cdot x\right)

(FPCore (x) :precision binary64 (* (* x 3.0) x))
↓
(FPCore (x) :precision binary64 (* x (* 3.0 x)))
double code(double x) {
	return (x * 3.0) * x;
}
↓
double code(double x) {
	return x * (3.0 * x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded in x around 0 0.2

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

  3. Applied add-cube-cbrt_binary640.2

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)} \cdot {x}^{2} \]

  4. Applied associate-*l*_binary640.3

    \[\leadsto \color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot {x}^{2}\right)} \]

  5. Applied unpow2_binary640.3

    \[\leadsto \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

  6. Applied associate-*r*_binary640.3

    \[\leadsto \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{3} \cdot x\right) \cdot x\right)} \]

  7. Applied associate-*r*_binary640.3

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot x\right)\right) \cdot x} \]

  8. Simplified0.2

    \[\leadsto \color{blue}{\left(3 \cdot x\right)} \cdot x \]

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2022160 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))