Average Error: 0.0 → 0.0
Time: 37.9s
Precision: 64
Internal Precision: 128
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - \left(mu - EAccept\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{\left(Vef + EDonor\right) + \left(mu - Ec\right)}{KbT}} + 1}\]

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. Initial simplification0.0

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

  4. Applied add-log-exp0.0

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

  5. Applied rem-exp-log0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2018362 
(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: 32.2s)Debug log

start125.0ms

Algorithm
intervals

setup421.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

18.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
15.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
9.0ms
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))

series360.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

181.0ms
(/ NaChar (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))))
75.0ms
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
54.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
48.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

simplify5.6s

Counts
42 → 83
Calls

42 calls. Slowest were:

622.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 1))) (/ mu KbT))
379.0ms
(+ (* (- (* mu mu) (* Ec Ec)) (- Vef EDonor)) (* (+ mu Ec) (- (* Vef Vef) (* EDonor EDonor))))
309.0ms
(+ (* 1 1) (- (* (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)) (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))) (* 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))))

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

17.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
11.0ms
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
9.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

series311.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

154.0ms
(/ NaChar (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))))
62.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
56.0ms
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
38.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

simplify5.9s

Counts
42 → 83
Calls

42 calls. Slowest were:

650.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 1))) (/ mu KbT))
357.0ms
(+ (* (- (* mu mu) (* Ec Ec)) (- Vef EDonor)) (* (+ mu Ec) (- (* Vef Vef) (* EDonor EDonor))))
329.0ms
(- (+ (/ Ev KbT) (+ (/ EAccept KbT) (+ 1 (/ Vef KbT)))) (/ mu KbT))

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))) NaChar))
0.0b
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
0.0b
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
0.0b
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

rewrite45.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

16.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
13.0ms
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
11.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

series377.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

205.0ms
(/ 1 (/ (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))) NaChar))
66.0ms
(exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
65.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
41.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

simplify5.6s

Counts
42 → 86
Calls

42 calls. Slowest were:

594.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 1))) (/ mu KbT))
455.0ms
(- (* (- (* Ev Ev) (* Vef Vef)) (+ (* mu mu) (+ (* EAccept EAccept) (* mu EAccept)))) (* (- Ev Vef) (- (pow mu 3) (pow EAccept 3))))
393.0ms
(+ (* (- (* mu mu) (* Ec Ec)) (- Vef EDonor)) (* (+ mu Ec) (- (* Vef Vef) (* EDonor EDonor))))

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

9.1b
(sqrt (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
9.1b
(sqrt (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
0.0b
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
0.0b
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

21.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
17.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)
6.0ms
(sqrt (/ (- (+ Ev Vef) (- mu EAccept)) KbT))

series375.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

142.0ms
(sqrt (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
131.0ms
(sqrt (/ (- (+ Ev Vef) (- mu EAccept)) KbT))
58.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
44.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

simplify3.6s

Counts
43 → 83
Calls

43 calls. Slowest were:

354.0ms
(+ (* (- (* mu mu) (* Ec Ec)) (- Vef EDonor)) (* (+ mu Ec) (- (* Vef Vef) (* EDonor EDonor))))
209.0ms
(- (* (+ Ev Vef) (+ Ev Vef)) (* (- mu EAccept) (- mu EAccept)))
204.0ms
(sqrt (sqrt (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes807.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch5.0ms