Average Error: 0.2 → 0.5
Time: 3.1s
Precision: 64
\[\left(x \cdot 3\right) \cdot x\]
↓
\[\left({\left(\sqrt{\sqrt{\left(x \cdot 3\right) \cdot x}}\right)}^{\frac{3}{2}} \cdot \sqrt{\left(x \cdot 3\right) \cdot x}\right) \cdot \sqrt{\sqrt{\sqrt{\left(x \cdot 3\right) \cdot x}}}\]
\left(x \cdot 3\right) \cdot x
↓
\left({\left(\sqrt{\sqrt{\left(x \cdot 3\right) \cdot x}}\right)}^{\frac{3}{2}} \cdot \sqrt{\left(x \cdot 3\right) \cdot x}\right) \cdot \sqrt{\sqrt{\sqrt{\left(x \cdot 3\right) \cdot x}}}
double f(double x) {
        double r212632 = x;
        double r212633 = 3.0;
        double r212634 = r212632 * r212633;
        double r212635 = r212634 * r212632;
        return r212635;
}
↓
double f(double x) {
        double r212636 = x;
        double r212637 = 3.0;
        double r212638 = r212636 * r212637;
        double r212639 = r212638 * r212636;
        double r212640 = sqrt(r212639);
        double r212641 = sqrt(r212640);
        double r212642 = 1.5;
        double r212643 = pow(r212641, r212642);
        double r212644 = r212643 * r212640;
        double r212645 = sqrt(r212641);
        double r212646 = r212644 * r212645;
        return r212646;
}

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-sqrt0.4

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

  5. Applied add-sqr-sqrt0.5

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

  6. Applied associate-*r*0.5

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

  7. Simplified0.7

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

  9. Applied add-sqr-sqrt0.7

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

  10. Applied sqrt-prod0.7

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

  11. Applied associate-*r*0.7

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

  12. Simplified0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3) x))