Average Error: 0.0 → 0.0
Time: 42.0s
Precision: 64
Internal Precision: 128
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{e^{\left(\left(Ev + EAccept\right) - \left(mu - Vef\right)\right) \cdot \frac{1}{KbT}} + 1} + \frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}}\]

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

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

  4. Applied div-inv0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 
(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: 36.7s)Debug log

start89.0ms

Algorithm
intervals

setup355.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
4 → 68
Calls

4 calls. Slowest were:

10.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
8.0ms
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)
5.0ms
(+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT)))

series331.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

169.0ms
(/ NaChar (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))))
65.0ms
(+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT)))
51.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
46.0ms
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)

simplify5.9s

Counts
36 → 80
Calls

36 calls. Slowest were:

725.0ms
(+ (* (- (pow Vef 3) (pow Ec 3)) (- EDonor mu)) (* (+ (* Vef Vef) (+ (* Ec Ec) (* Vef Ec))) (- (* EDonor EDonor) (* mu mu))))
676.0ms
(- (+ (* 1/4 (/ (* mu NaChar) KbT)) (* 1/2 NaChar)) (+ (* 1/4 (/ (* EAccept NaChar) KbT)) (+ (* 1/4 (/ (* Ev NaChar) KbT)) (* 1/4 (/ (* Vef NaChar) KbT)))))
549.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 2))) (/ mu KbT))

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT))
0.0b
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
0.0b
(/ NaChar (+ 1 (exp (* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT)))))
0.0b
(+ 1 (exp (* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
4 → 80
Calls

4 calls. Slowest were:

10.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
10.0ms
(* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT))
1.0ms
(+ 1 (exp (* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT))))

series346.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

167.0ms
(/ NaChar (+ 1 (exp (* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT)))))
81.0ms
(+ 1 (exp (* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT))))
60.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
38.0ms
(* (- (+ EAccept Ev) (- mu Vef)) (/ 1 KbT))

simplify9.1s

Counts
54 → 92
Calls

54 calls. Slowest were:

619.0ms
(+ (* (- (pow Vef 3) (pow Ec 3)) (- EDonor mu)) (* (+ (* Vef Vef) (+ (* Ec Ec) (* Vef Ec))) (- (* EDonor EDonor) (* mu mu))))
523.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 2))) (/ mu KbT))
519.0ms
(- (+ (/ Ev KbT) (+ (/ EAccept KbT) (+ 2 (/ Vef KbT)))) (/ mu KbT))

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

20.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
16.0ms
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)
6.0ms
(/ 1 (/ (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))) NaChar))

series439.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

270.0ms
(/ 1 (/ (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))) NaChar))
59.0ms
(+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT)))
55.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
55.0ms
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)

simplify4.8s

Counts
36 → 83
Calls

36 calls. Slowest were:

609.0ms
(+ (* (- (pow Vef 3) (pow Ec 3)) (- EDonor mu)) (* (+ (* Vef Vef) (+ (* Ec Ec) (* Vef Ec))) (- (* EDonor EDonor) (* mu mu))))
569.0ms
(- (+ (/ Ev KbT) (+ (/ EAccept KbT) (+ 2 (/ Vef KbT)))) (/ mu KbT))
555.0ms
(- (+ (/ Ev KbT) (+ (/ Vef KbT) (+ (/ EAccept KbT) 2))) (/ mu KbT))

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))))
0.1b
(/ 1 (/ (exp (log (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))))) NaChar))
0.0b
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)
0.0b
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)

rewrite53.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

21.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
16.0ms
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)
8.0ms
(/ 1 (/ (exp (log (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))))) NaChar))

series551.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

263.0ms
(/ 1 (/ (exp (log (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))))) NaChar))
164.0ms
(log (+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT))))
64.0ms
(/ (+ (- Vef Ec) (+ EDonor mu)) KbT)
60.0ms
(/ (- (+ EAccept Ev) (- mu Vef)) KbT)

simplify5.2s

Counts
42 → 87
Calls

42 calls. Slowest were:

745.0ms
(+ (* (- (pow Vef 3) (pow Ec 3)) (- EDonor mu)) (* (+ (* Vef Vef) (+ (* Ec Ec) (* Vef Ec))) (- (* EDonor EDonor) (* mu mu))))
349.0ms
(+ (* (- (* Vef Vef) (* Ec Ec)) (- EDonor mu)) (* (+ Vef Ec) (- (* EDonor EDonor) (* mu mu))))
244.0ms
(+ 1 (exp (/ (- (+ EAccept Ev) (- mu Vef)) KbT)))

prune2.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes749.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms