Average Error: 0.0 → 0.0
Time: 1.3m
Precision: 64
Internal Precision: 128
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{\sqrt[3]{\left(Vef + EDonor\right) + \left(mu - Ec\right)} \cdot \sqrt[3]{\left(Vef + EDonor\right) + \left(mu - Ec\right)}}{\frac{KbT}{\sqrt[3]{\left(Vef + EDonor\right) + \left(mu - Ec\right)}}}}} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - \left(mu - EAccept\right)}{KbT}} + 1}\]

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-cube-cbrt0.0

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

  5. Applied associate-/l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 
(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: 1.3m)Debug log

sample71.0ms

Algorithm
intervals

simplify297.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

297.0ms
(+ (/ NdChar (+ 1 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Counts
4 → 68
Calls

4 calls. Slowest were:

34.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
18.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
8.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

series308.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

129.0ms
(/ NaChar (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))))
83.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
51.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)
45.0ms
(/ (- (+ Ev Vef) (- mu EAccept)) KbT)

simplify5.0s

Counts
36 → 80
Calls

36 calls. Slowest were:

600.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
506.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
347.0ms
(+ (* (- (* mu mu) (* Ec Ec)) (- Vef EDonor)) (* (+ mu Ec) (- (* Vef Vef) (* EDonor EDonor))))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (- mu Ec) (+ Vef EDonor)))
0.5b
(cbrt (+ (- mu Ec) (+ Vef EDonor)))
0.5b
(cbrt (+ (- mu Ec) (+ Vef EDonor)))
0.5b
(* (cbrt (+ (- mu Ec) (+ Vef EDonor))) (cbrt (+ (- mu Ec) (+ Vef EDonor))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Counts
4 → 132
Calls

4 calls. Slowest were:

23.0ms
(* (cbrt (+ (- mu Ec) (+ Vef EDonor))) (cbrt (+ (- mu Ec) (+ Vef EDonor))))
2.0ms
(cbrt (+ (- mu Ec) (+ Vef EDonor)))
2.0ms
(cbrt (+ (- mu Ec) (+ Vef EDonor)))

series935.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

239.0ms
(cbrt (+ (- mu Ec) (+ Vef EDonor)))
237.0ms
(* (cbrt (+ (- mu Ec) (+ Vef EDonor))) (cbrt (+ (- mu Ec) (+ Vef EDonor))))
235.0ms
(cbrt (+ (- mu Ec) (+ Vef EDonor)))
225.0ms
(cbrt (+ (- mu Ec) (+ Vef EDonor)))

simplify22.4s

Counts
148 → 144
Calls

148 calls. Slowest were:

631.0ms
(* (+ (- mu Ec) (+ Vef EDonor)) (+ (- mu Ec) (+ Vef EDonor)))
615.0ms
(cbrt (+ (* (- (* mu mu) (* Ec Ec)) (- Vef EDonor)) (* (+ mu Ec) (- (* Vef Vef) (* EDonor EDonor)))))
544.0ms
(* (+ (- mu Ec) (+ Vef EDonor)) (+ (- mu Ec) (+ Vef EDonor)))

prune5.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Counts
4 → 112
Calls

4 calls. Slowest were:

35.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
14.0ms
(/ (/ NaChar (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))))) (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))))
10.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

series470.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

176.0ms
(/ NaChar (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))))
149.0ms
(/ (/ NaChar (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))))) (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))))
89.0ms
(+ (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)
56.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

simplify18.1s

Counts
115 → 124
Calls

115 calls. Slowest were:

360.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
358.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
268.0ms
(- (log (/ NaChar (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT)))))) (log (sqrt (+ 1 (exp (/ (- (+ Ev Vef) (- mu EAccept)) KbT))))))

prune2.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))
0.2b
(+ (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT))) (- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)))
0.2b
(/ (+ (pow (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 3) (pow 1 3)) (+ (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT))) (- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))))
0.0b
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

rewrite458.0ms

Algorithm
rewrite-expression-head
Counts
4 → 104
Calls

4 calls. Slowest were:

402.0ms
(/ (+ (pow (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 3) (pow 1 3)) (+ (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT))) (- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))))
42.0ms
(+ (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT))) (- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)))
10.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

series706.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

497.0ms
(/ (+ (pow (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 3) (pow 1 3)) (+ (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT))) (- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))))
120.0ms
(+ (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT))) (- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1)))
52.0ms
(- (* 1 1) (* (exp (/ (+ (- mu Ec) (+ Vef EDonor)) KbT)) 1))
37.0ms
(/ (+ (- mu Ec) (+ Vef EDonor)) KbT)

simplify13.4s

Counts
94 → 116
Calls

94 calls. Slowest were:

352.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 2))) (/ Ec KbT))
351.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 1))) (/ Ec KbT))
351.0ms
(- (+ (/ mu KbT) (+ (/ Vef KbT) (+ (/ EDonor KbT) 1))) (/ Ec KbT))

prune2.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes561.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.1s

Algorithm
intervals