Average Error: 39.4 → 0.1
Time: 13.0s
Precision: 64
Internal Precision: 1344
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{e^{x} + 1}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.4

    \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]

  2. Initial simplification0.1

    \[\leadsto \sqrt{e^{x} + 1}\]

  3. Final simplification0.1

    \[\leadsto \sqrt{e^{x} + 1}\]

Runtime

Time bar (total: 13.0s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.10.10.00.00%
herbie shell --seed 2018286 +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))