Average Error: 0.2 → 0.2
Time: 2.0s
Precision: binary64
\[\left(x \cdot 3\right) \cdot x\]
↓
\[3 \cdot \left(x \cdot x\right)\]
\left(x \cdot 3\right) \cdot x
↓
3 \cdot \left(x \cdot x\right)
(FPCore (x) :precision binary64 (* (* x 3.0) x))
↓
(FPCore (x) :precision binary64 (* 3.0 (* x x)))
double code(double x) {
	return (x * 3.0) * x;
}
↓
double code(double x) {
	return 3.0 * (x * 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. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_72610.4

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

  4. Simplified0.4

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

  5. Simplified0.4

    \[\leadsto \sqrt{x \cdot \left(x \cdot 3\right)} \cdot \color{blue}{\sqrt{x \cdot \left(x \cdot 3\right)}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt_binary64_72610.4

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

  8. Simplified0.3

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

  9. Simplified0.5

    \[\leadsto \left|x \cdot \sqrt{3}\right| \cdot \color{blue}{\left|x \cdot \sqrt{3}\right|}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt_binary64_72740.2

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

  12. Applied associate-*r*_binary64_71790.3

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

  13. Taylor expanded around 0 0.5

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

  14. Simplified0.2

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

  15. Final simplification0.2

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

Reproduce

herbie shell --seed 2020346 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))