Average Error: 39.9 → 0.5
Time: 6.9s
Precision: 64
Internal Precision: 1344
\[\frac{e^{x}}{e^{x} - 1}\]
↓
\[\frac{1}{\frac{(e^{x} - 1)^*}{e^{x}}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original39.9
Target39.4
Herbie0.5
\[\frac{1}{1 - e^{-x}}\]

Derivation

  1. Initial program 39.9

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

  2. Initial simplification0.5

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

  4. Applied clear-num0.5

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

  5. Final simplification0.5

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

Runtime

Time bar (total: 6.9s)Debug logProfile

herbie shell --seed 2018230 +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

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

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