Average Error: 0.5 → 0.5
Time: 8.7s
Precision: 64
Internal Precision: 576
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x} \cdot \sqrt{x + -1}\]

Error

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Results

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Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Initial simplification0.5

    \[\leadsto \sqrt{x + -1} \cdot \sqrt{x}\]
  3. Using strategy rm

  4. Applied *-commutative0.5

    \[\leadsto \color{blue}{\sqrt{x} \cdot \sqrt{x + -1}}\]

  5. Final simplification0.5

    \[\leadsto \sqrt{x} \cdot \sqrt{x + -1}\]

Runtime

Time bar (total: 8.7s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.50.50.00.50%
herbie shell --seed 2018339 
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))