Details

Time bar (total: 6.1s)

sample138.0ms

Algorithm
intervals
Results
56.0ms43×body2560valid
48.0ms95×body1280valid
17.0ms66×body640valid
5.0ms30×body320valid
2.0ms11×body160valid
1.0ms11×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0167
1167

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.9b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
1.3b
(- 1.0 (cos x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series11.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

simplify47.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
05700608

prune124.0ms

Filtered
42 candidates to 58 candidates (-38.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New441458
Fresh000
Picked101
Done000
Total451459

Merged error: 0.2b

Counts
59 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b
(exp (log (- 1.0 (cos x))))
0.4b
(log (- 1.0 (cos x)))
1.3b
(- 1.0 (cos x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
30×log-prod
25×exp-sum
24×add-cube-cbrt times-frac
8×associate-/l*
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-div add-cbrt-cube add-log-exp
4×exp-prod flip3-- exp-diff flip--
3×associate-/r*
2×log-pow associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num div-inv rem-exp-log
Counts
4 → 98
Calls
4 calls:
7.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
4.0ms
(exp (log (- 1.0 (cos x))))
3.0ms
(log (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series26.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms
(exp (log (- 1.0 (cos x))))
12.0ms
(log (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

simplify40.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
050491090

prune150.0ms

Filtered
64 candidates to 110 candidates (-71.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1055110
Fresh31013
Picked101
Done000
Total10915124

Merged error: 0.2b

Counts
124 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.0b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b
(- 1.0 (cos x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt *-un-lft-identity
45×times-frac
38×exp-prod
33×add-cube-cbrt
20×log-pow
11×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
3×log-prod div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms
(- 1.0 (cos x))

series29.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
10.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms
(- 1.0 (cos x))

simplify69.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
052311218

prune197.0ms

Filtered
89 candidates to 124 candidates (-39.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1195124
Fresh5914
Picked101
Done000
Total12514139

Merged error: 0.2b

Counts
139 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (sin x))
0.1b
(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.3b
(- 1.0 (cos x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
20×times-frac
19×add-cube-cbrt
16×add-exp-log
13×associate-*r*
10×add-cbrt-cube
6×pow1
5×associate-*l* add-log-exp
4×div-exp prod-exp
3×flip3-- associate-/r* flip-- associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
3 → 87
Calls
3 calls:
3.0ms
(/ 1 (sin x))
9.0ms
(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms
(- 1.0 (cos x))

series14.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(/ 1 (sin x))
7.0ms
(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms
(- 1.0 (cos x))

simplify29.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
05227781

prune79.0ms

Filtered
60 candidates to 96 candidates (-60.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New95196
Fresh01313
Picked011
Done000
Total9515110

Merged error: 0.2b

Counts
110 → 15

regimes223.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch40.0ms

Steps
ItersRangePoint
10
0.009091900342010817
66730311810763.45
0.022272457972738604
9
-60.40944958396893
-2.7804654585538832e-05
-0.024260903871319413

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03843
13843

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.4s1618×body2560valid
1.4s2813×body1280valid
476.0ms1800×body640valid
178.0ms938×body320valid
65.0ms460×body160valid
38.0ms7×body5120valid
28.0ms364×body80valid

Profiling

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