Details

Time bar (total: 43.0s)

sample334.0ms

Algorithm
intervals
Results
10.0ms191×body80valid
8.0ms32×body2560valid
6.0ms30×body1280valid
4.0ms97×body80nan
2.0ms14×body640valid
1.0msbody5120valid
1.0msbody320valid
0.0msbody160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

prune6.0ms

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: 33.2b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b
(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
21.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
add-exp-log add-cbrt-cube
pow1 distribute-rgt-neg-in associate-/l*
associate-/r* sqrt-prod
neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
10.0ms
(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series72.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms
(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(- (* b_2 b_2) (* a c))
23.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0338783
11216724
24971703
35001703

prune413.0ms

Filtered
92 candidates to 69 candidates (25.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New821092
Fresh000
Picked011
Done000
Total821193

Merged error: 5.1b

Counts
93 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.0b
(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.9b
(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
flip3-- flip--
div-inv add-log-exp
pow1
cbrt-undiv div-exp
associate-/l/
frac-2neg sqrt-div clear-num
sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 200
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
41.0ms
(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
54.0ms
(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07083365
132313197
250013171

prune1.4s

Filtered
212 candidates to 142 candidates (33.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2102212
Fresh369
Picked101
Done011
Total2149223

Merged error: 5.1b

Counts
223 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
2.1b
(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0b
(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
585×add-sqr-sqrt
584×*-un-lft-identity
392×add-cube-cbrt
96×distribute-lft-out-- difference-of-squares
83×associate-/l*
51×sqrt-prod
48×distribute-rgt-neg-in
28×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
cbrt-undiv div-exp
add-log-exp
pow1 associate-/r/
flip3-- frac-2neg sqrt-div clear-num flip--
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 485
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
29.0ms
(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
52.0ms
(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
42.0ms
(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015258628
150017984

prune4.8s

Filtered
497 candidates to 298 candidates (40.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4961497
Fresh167
Picked101
Done011
Total4988506

Merged error: 5.1b

Counts
506 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
1.3b
(/ (/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
21.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
2862×times-frac
1645×add-sqr-sqrt
1644×*-un-lft-identity
1136×add-cube-cbrt
993×cbrt-prod
254×distribute-lft-out-- difference-of-squares
155×associate-/l*
130×sqrt-prod
127×distribute-rgt-neg-in
50×div-inv
13×add-exp-log
10×add-log-exp
add-cbrt-cube
associate-/r/
cbrt-undiv div-exp associate-/r*
pow1
flip3-- diff-log flip--
sub-neg sqrt-div
associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 1153
Calls
4 calls:
8.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
52.0ms
(/ (/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series84.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(- (* b_2 b_2) (* a c))
50.0ms
(/ (/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify267.0ms

Algorithm
egg-herbie
Counts
1165 → 1165
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0292327910
1500126669

prune32.5s

Filtered
1165 candidates to 678 candidates (41.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New116501165
Fresh066
Picked011
Done011
Total116581173

Merged error: 5.1b

Counts
1173 → 8

regimes456.0ms

Accuracy

93.7% (1.6b remaining)

Error of 7.3b against oracle of 5.7b and baseline of 31.0b

bsearch218.0ms

Steps
ItersRangePoint
10
4.2917270207488e+96
9.615152778888747e+106
5.2249784563665464e+104
10
1.5449499907901935e-212
3.426440312001654e-201
1.610651904509826e-212
9
-1.3279209152234913e+54
-5.495259451600425e+45
-1.307112579275623e+54

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326
14526
24526

end0.0ms

sample1.3s

Algorithm
intervals
Results
261.0ms1066×body2560valid
246.0ms5871×body80valid
167.0ms853×body1280valid
112.0ms2842×body80nan
69.0ms450×body640valid
30.0ms246×body320valid
30.0ms97×body5120valid
10.0ms124×body160valid

Profiling

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