Average Error: 0.5 → 0.7
Time: 23.7s
Precision: 64
Internal Precision: 576
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1} \cdot \left(\sqrt{\sqrt{x}} \cdot \sqrt{\sqrt{x}}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

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

  3. Applied add-sqr-sqrt0.7

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

  4. Applied associate-*r*0.7

    \[\leadsto \color{blue}{\left(\sqrt{x - 1} \cdot \sqrt{\sqrt{x}}\right) \cdot \sqrt{\sqrt{x}}}\]
  5. Using strategy rm

  6. Applied associate-*l*0.7

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

  7. Final simplification0.7

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

Runtime

Time bar (total: 23.7s)Debug logProfile

herbie shell --seed 2018220 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))