Details

Time bar (total: 3.4s)

sample56.0ms

Algorithm
intervals
Results
25.0ms53×body2560valid
10.0ms44×body1280valid
8.0ms53×body640valid
3.0ms29×body320valid
2.0ms64×body80valid
1.0ms13×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

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: 33.9b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b
(- 1.0 (cos x))
16.4b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
48.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify66.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune135.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New361248
Fresh000
Picked101
Done000
Total371249

Merged error: 0.1b

Counts
49 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.6b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series106.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 1/720 (pow x 4))
24.0ms
(* 1/24 (pow x 2))
46.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify45.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0268345
11132313
25001307

prune136.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New74175
Fresh11011
Picked011
Done000
Total751287

Merged error: 0.1b

Counts
87 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
1.6b
(log (exp (* 1/24 (pow x 2))))
22.6b
(- (+ (* 1/720 (pow x 4)) 1/2) (log (exp (* 1/24 (pow x 2)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
15×*-un-lft-identity associate-*r*
14×add-exp-log
12×add-cube-cbrt
8×unpow-prod-down add-cbrt-cube add-log-exp
7×unswap-sqr
6×pow1 log-prod associate-*l* prod-exp
4×log-pow sqr-pow
3×associate--r+
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod distribute-lft-out-- unpow2
1×sub-neg exp-prod flip3-- exp-to-pow rem-log-exp associate--l+ sum-log flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
2.0ms
(log (exp (* 1/24 (pow x 2))))
9.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (log (exp (* 1/24 (pow x 2)))))

series138.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* 1/720 (pow x 4))
24.0ms
(* 1/24 (pow x 2))
30.0ms
(log (exp (* 1/24 (pow x 2))))
43.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (log (exp (* 1/24 (pow x 2)))))

simplify42.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0305496
11195433
25002429

prune195.0ms

Filtered
98 candidates to 61 candidates (62.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New98098
Fresh01010
Picked011
Done011
Total9812110

Merged error: 0.1b

Counts
110 → 12

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.7b
(- 1.0 (cos x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 114
Calls
3 calls:
14.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series106.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
46.0ms
(/ (- 1.0 (cos x)) x)
18.0ms
(- 1.0 (cos x))

simplify62.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0521814
12334726
25001690

prune169.0ms

Filtered
123 candidates to 81 candidates (65.9%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1203123
Fresh369
Picked101
Done022
Total12411135

Merged error: 0.1b

Counts
135 → 11

regimes101.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.7b

bsearch61.0ms

Steps
ItersRangePoint
9
2.8262556577633816e-09
1.3569245790634763
0.03231226303240678
7
-5.155753157609302
-0.022529268385055725
-0.035840091652124574

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14024

end0.0ms

sample1.8s

Algorithm
intervals
Results
753.0ms1578×body2560valid
478.0ms1299×body1280valid
246.0ms1531×body640valid
101.0ms903×body320valid
75.0ms2234×body80valid
35.0ms455×body160valid

Profiling

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