Details

Time bar (total: 3.1s)

sample30.0ms

Algorithm
intervals
Results
9.0ms45×body1280valid
6.0ms43×body640valid
4.0ms136×body80valid
2.0ms17×body320valid
1.0ms15×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.7b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
3.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite24.0ms

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:
9.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
11.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
19.0ms
(+ 1.0 (exp (* -2.0 x)))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify90.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0251494
1731465
22785460
35002460

prune149.0ms

Filtered
69 candidates to 50 candidates (72.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh000
Picked101
Done000
Total67370

Merged error: 0b

Counts
70 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
0.0b
(+ (exp (* -2.0 x)) 1.0)
3.6b
(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

rewrite22.0ms

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:
6.0ms
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
4.0ms
(+ (exp (* -2.0 x)) 1.0)
11.0ms
(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

series135.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
19.0ms
(+ (exp (* -2.0 x)) 1.0)
79.0ms
(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0248495
1705465
22762458
35002458

prune137.0ms

Filtered
69 candidates to 48 candidates (69.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New68169
Fresh112
Picked011
Done000
Total69372

Merged error: 0b

Counts
72 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp (* -2.0 x)) 1.0)
0.0b
(+ (exp (* -2.0 x)) 1.0)
0.3b
(* (+ (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0)))
4.1b
(- (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
22×*-un-lft-identity
20×sqrt-prod
12×difference-of-squares
11×associate-*r*
10×add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×flip3-+ associate-*l* flip-+
4×frac-times flip3-- times-frac flip-- distribute-lft-out distribute-lft-out--
3×sub-neg
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 84
Calls
4 calls:
4.0ms
(+ (exp (* -2.0 x)) 1.0)
6.0ms
(+ (exp (* -2.0 x)) 1.0)
32.0ms
(* (+ (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0)))
15.0ms
(- (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0))

series530.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (exp (* -2.0 x)) 1.0)
17.0ms
(+ (exp (* -2.0 x)) 1.0)
380.0ms
(* (+ (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0)))
117.0ms
(- (sqrt (/ 2.0 (+ (exp (* -2.0 x)) 1.0))) (sqrt 1.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03871297
116821150
250011121

prune238.0ms

Filtered
96 candidates to 66 candidates (68.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New96096
Fresh011
Picked011
Done011
Total96399

Merged error: 0b

Counts
99 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 0.33333333333333337 (pow x 3))
7.6b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×pow1 sqr-pow
1×+-commutative cube-mult pow-to-exp flip3-+ unpow3 pow-exp sum-log *-commutative cbrt-unprod flip-+
Counts
2 → 42
Calls
2 calls:
6.0ms
(* 0.33333333333333337 (pow x 3))
4.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series139.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 0.33333333333333337 (pow x 3))
104.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify34.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0199228
1849205
25001204

prune105.0ms

Filtered
48 candidates to 30 candidates (62.5%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New48048
Fresh000
Picked011
Done022
Total48351

Merged error: 0b

Counts
51 → 3

regimes142.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03514
13514

end0.0ms

sample864.0ms

Algorithm
intervals
Results
355.0ms1709×body1280valid
180.0ms1246×body640valid
107.0ms4079×body80valid
56.0ms605×body320valid
24.0ms361×body160valid