Average Error: 40.1 → 0.4
Time: 11.3s
Precision: 64
Internal Precision: 128
\[\frac{e^{x}}{e^{x} - 1}\]
↓
\[e^{x} \cdot \frac{1}{(e^{x} - 1)^*}\]

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original40.1
Target39.7
Herbie0.4
\[\frac{1}{1 - e^{-x}}\]

Derivation

  1. Initial program 40.1

    \[\frac{e^{x}}{e^{x} - 1}\]

  2. Initial simplification0.4

    \[\leadsto \frac{e^{x}}{(e^{x} - 1)^*}\]
  3. Using strategy rm

  4. Applied div-inv0.4

    \[\leadsto \color{blue}{e^{x} \cdot \frac{1}{(e^{x} - 1)^*}}\]

  5. Final simplification0.4

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

Runtime

Time bar (total: 11.3s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.40.40.40.00%
herbie shell --seed 2018353 +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

  :herbie-target
  (/ 1 (- 1 (exp (- x))))

  (/ (exp x) (- (exp x) 1)))