Average Error: 39.3 → 0.1
Time: 2.9m
Precision: 64
Internal Precision: 1344
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{\frac{(e^{x + x} - 1)^*}{(e^{x} - 1)^*}}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.3

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

  2. Initial simplification0.1

    \[\leadsto \sqrt{\frac{(e^{x + x} - 1)^*}{(e^{x} - 1)^*}}\]

  3. Final simplification0.1

    \[\leadsto \sqrt{\frac{(e^{x + x} - 1)^*}{(e^{x} - 1)^*}}\]

Runtime

Time bar (total: 2.9m)Debug logProfile

herbie shell --seed 2018214 +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))