Average Error: 0.5 → 0.8
Time: 32.2s
Precision: 64
Internal Precision: 576
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}} \cdot \left(\sqrt{\sqrt[3]{x - 1}} \cdot \sqrt{x}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.9

    \[\leadsto \sqrt{\color{blue}{\left(\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}\right) \cdot \sqrt[3]{x - 1}}} \cdot \sqrt{x}\]

  4. Applied sqrt-prod0.9

    \[\leadsto \color{blue}{\left(\sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}} \cdot \sqrt{\sqrt[3]{x - 1}}\right)} \cdot \sqrt{x}\]

  5. Applied associate-*l*0.8

    \[\leadsto \color{blue}{\sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}} \cdot \left(\sqrt{\sqrt[3]{x - 1}} \cdot \sqrt{x}\right)}\]

Runtime

Time bar (total: 32.2s)Debug logProfile

herbie shell --seed '#(1071119240 1686926585 3481876196 78132896 2080707795 3185793749)' 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))