Average Error: 0.2 → 0.2
Time: 2.5s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left({x}^{2} \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}} + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left({x}^{2} \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}} + \left(-2 \cdot {x}^{3}\right)
double code(double x) {
	return ((x * x) * (3.0 - (x * 2.0)));
}
↓
double code(double x) {
	return (((pow(x, 2.0) * (pow(cbrt(3.0), 2.0) * cbrt((cbrt(3.0) * cbrt(3.0))))) * cbrt(cbrt(3.0))) + -(2.0 * pow(x, 3.0)));
}

Error

Bits error versus x

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.1

    \[\leadsto \left(x \cdot x\right) \cdot 3 + \color{blue}{\left(-2 \cdot {x}^{3}\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.1

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

  8. Applied associate-*r*0.2

    \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}} + \left(-2 \cdot {x}^{3}\right)\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.2

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

  11. Applied cbrt-prod0.2

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

  12. Applied associate-*r*0.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3 (* x 2))))

  (* (* x x) (- 3 (* x 2))))