Details

Time bar (total: 7.4s)

sample39.0ms

Algorithm
intervals
Results
13.0ms52×body1280valid
5.0ms34×body640valid
4.0ms135×body80valid
3.0ms24×body320valid
1.0ms11×body160valid

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.9b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
4.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
13×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×associate-/r*
3×pow1 associate-/l*
2×flip3-+ associate-/r/ flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
3 → 60
Calls
3 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series162.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(+ 1.0 (exp (* -2.0 x)))
45.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
97.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify92.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22771460
35002460

prune218.0ms

Filtered
69 candidates to 50 candidates (27.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh000
Picked101
Done000
Total67370

Merged error: 0.0b

Counts
70 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
0.1b
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
4.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
37×*-un-lft-identity
19×add-cube-cbrt
18×cbrt-prod
17×times-frac
12×unpow-prod-down cube-prod
10×difference-of-squares
7×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1 distribute-lft-out--
4×cube-div associate-/r* distribute-lft-out
3×pow-unpow flip3-- flip-- associate-/l*
2×cube-mult cbrt-div unpow3 associate-/r/ sqr-pow
1×cbrt-undiv pow-to-exp sub-neg pow-pow frac-2neg flip3-+ pow1/3 diff-log div-exp pow-exp clear-num rem-cbrt-cube flip-+ div-inv rem-cube-cbrt
Counts
4 → 108
Calls
4 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
10.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
9.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series389.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
151.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
99.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
96.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03821080
114221033
250011019

prune441.0ms

Filtered
120 candidates to 71 candidates (40.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1191120
Fresh112
Picked011
Done000
Total1203123

Merged error: 0.0b

Counts
123 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
0.1b
(cbrt (* (pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
0.3b
(pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
5.2b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
121×add-sqr-sqrt
39×sqrt-prod
34×associate-*r*
30×unpow-prod-down cube-prod difference-of-squares
27×*-un-lft-identity
26×cube-div
24×times-frac
17×add-exp-log
16×unswap-sqr
14×associate-*l*
13×add-cube-cbrt
11×sqr-pow
9×prod-exp
8×frac-times cbrt-div
7×pow-to-exp flip3-- flip3-+ pow-exp add-cbrt-cube flip-- flip-+
6×add-log-exp
5×pow1
4×associate-*r/ associate-*l/ distribute-lft-out
3×cube-mult pow-unpow unpow3 distribute-lft-out--
2×pow-prod-down
1×cbrt-prod sub-neg pow-pow pow1/3 diff-log *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 159
Calls
4 calls:
61.0ms
(* (pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
48.0ms
(cbrt (* (pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
24.0ms
(pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
25.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
789.0ms
(* (pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
464.0ms
(cbrt (* (pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3) (pow (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
336.0ms
(pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
146.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify147.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
07254124
139283856
250023747

prune849.0ms

Filtered
171 candidates to 92 candidates (46.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1701171
Fresh011
Picked101
Done011
Total1713174

Merged error: 0.0b

Counts
174 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
5.2b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
5.2b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
5.2b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
39×sqrt-prod
30×difference-of-squares
24×times-frac
17×*-un-lft-identity
10×add-log-exp
7×add-cube-cbrt
5×pow1 add-exp-log add-cbrt-cube
4×unpow-prod-down cube-prod
3×sub-neg pow-unpow flip3-- diff-log flip-- distribute-lft-out--
2×cube-div distribute-lft-out
1×cube-mult pow-to-exp pow-pow flip3-+ unpow3 pow-exp flip-+ rem-cube-cbrt sqr-pow
Counts
4 → 96
Calls
4 calls:
23.0ms
(pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
23.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
25.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
23.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series762.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(pow (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
142.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
144.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
142.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03731674
115851589
250011584

prune466.0ms

Filtered
108 candidates to 58 candidates (46.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1080108
Fresh011
Picked011
Done011
Total1083111

Merged error: 0.0b

Counts
111 → 3

regimes526.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05081
15081

end0.0ms

sample1.1s

Algorithm
intervals
Results
405.0ms1702×body1280valid
197.0ms1230×body640valid
132.0ms4098×body80valid
78.0ms670×body320valid
21.0ms300×body160valid

Profiling

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