Average Error: 0.2 → 0.3
Time: 10.6s
Precision: 64
Internal Precision: 576
\[\log \left(\sin x\right) + \tanh x\]
\[\log \left(e^{\tanh x + \log \left(\sin x\right)}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\log \left(\sin x\right) + \tanh x\]
  2. Using strategy rm
  3. Applied add-log-exp0.2

    \[\leadsto \log \left(\sin x\right) + \color{blue}{\log \left(e^{\tanh x}\right)}\]
  4. Applied sum-log0.3

    \[\leadsto \color{blue}{\log \left(\sin x \cdot e^{\tanh x}\right)}\]
  5. Using strategy rm
  6. Applied add-exp-log0.3

    \[\leadsto \log \left(\color{blue}{e^{\log \left(\sin x\right)}} \cdot e^{\tanh x}\right)\]
  7. Applied prod-exp0.3

    \[\leadsto \log \color{blue}{\left(e^{\log \left(\sin x\right) + \tanh x}\right)}\]
  8. Final simplification0.3

    \[\leadsto \log \left(e^{\tanh x + \log \left(\sin x\right)}\right)\]

Runtime

Time bar (total: 10.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "log(sin(x)) + tanh(x)"
  (+ (log (sin x)) (tanh x)))