Average Error: 0.0 → 0.0
Time: 22.3s
Precision: 64
Internal Precision: 128
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{\sqrt[3]{\left(\left(e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1\right) \cdot \left(e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1\right)\right) \cdot \left(e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1\right)}} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - \left(mu - EAccept\right)}{KbT}} + 1}\]

Error

Bits error versus NdChar

Bits error versus Ec

Bits error versus Vef

Bits error versus EDonor

Bits error versus mu

Bits error versus KbT

Bits error versus NaChar

Bits error versus Ev

Bits error versus EAccept

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(Ev + Vef\right) - \left(mu - EAccept\right)}{KbT}}} + \frac{NdChar}{e^{\frac{\left(mu - Ec\right) + \left(Vef + EDonor\right)}{KbT}} + 1}}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube0.0

    \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(Ev + Vef\right) - \left(mu - EAccept\right)}{KbT}}} + \frac{NdChar}{\color{blue}{\sqrt[3]{\left(\left(e^{\frac{\left(mu - Ec\right) + \left(Vef + EDonor\right)}{KbT}} + 1\right) \cdot \left(e^{\frac{\left(mu - Ec\right) + \left(Vef + EDonor\right)}{KbT}} + 1\right)\right) \cdot \left(e^{\frac{\left(mu - Ec\right) + \left(Vef + EDonor\right)}{KbT}} + 1\right)}}}\]

  5. Final simplification0.0

    \[\leadsto \frac{NdChar}{\sqrt[3]{\left(\left(e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1\right) \cdot \left(e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1\right)\right) \cdot \left(e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1\right)}} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - \left(mu - EAccept\right)}{KbT}} + 1}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  (+ (/ NdChar (+ 1 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))

Details

Time bar (total: 21.7s)Debug log

sample89.0ms

Algorithm
intervals

simplify292.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

292.0ms
(+ (/ NdChar (+ 1 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
0.0b
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
0.0b
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
0.0b
(+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Counts
4 → 63
Calls

4 calls. Slowest were:

52.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
16.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
10.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

series260.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

91.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
71.0ms
(+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))
61.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
38.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

simplify4.5s

Counts
31 → 75
Calls

31 calls. Slowest were:

902.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
585.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 2))) (/ mu KbT))
530.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))

prune1.7s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
0.0b
(* (+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1) (+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))
0.0b
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
0.0b
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)

rewrite240.0ms

Algorithm
rewrite-expression-head
Counts
4 → 72
Calls

4 calls. Slowest were:

133.0ms
(* (+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1) (+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))
45.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
43.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)

series286.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

95.0ms
(* (+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1) (+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))
65.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
64.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
62.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

simplify8.9s

Counts
47 → 84
Calls

47 calls. Slowest were:

578.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
525.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
502.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))

prune2.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.0s

Algorithm
intervals