Average Error: 58.1 → 0.6
Time: 33.3s
Precision: 64
Internal Precision: 1344
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[\frac{(e^{x + x} - 1)^*}{e^{2 \cdot x} + 1}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied tanh-undef0.0

    \[\leadsto \color{blue}{\tanh x}\]
  4. Using strategy rm

  5. Applied tanh-def57.7

    \[\leadsto \color{blue}{\frac{e^{2 \cdot x} - 1}{e^{2 \cdot x} + 1}}\]

  6. Applied simplify0.6

    \[\leadsto \frac{\color{blue}{(e^{x + x} - 1)^*}}{e^{2 \cdot x} + 1}\]

Runtime

Time bar (total: 33.3s)Debug logProfile

herbie shell --seed 2018201 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))