Details

Time bar (total: 3.5s)

analyze226.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14

sample59.0ms

Algorithm
intervals
Results
27.0ms55×body2560valid
10.0ms38×body1280valid
8.0ms48×body640valid
3.0ms30×body320valid
2.0ms66×body80valid
2.0ms19×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.1b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.3b
(- 1.0 (cos x))
17.1b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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))

series9.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune90.0ms

Filtered
34 candidates to 48 candidates (-41.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New39948
Fresh000
Picked101
Done000
Total40949

Merged error: 0.1b

Counts
49 → 9

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)
2.3b
(- 1.0 (cos x))

rewrite28.0ms

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))

series17.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms
(/ (- 1.0 (cos x)) x)
6.0ms
(- 1.0 (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0521814
12334726
25001690

prune134.0ms

Filtered
80 candidates to 123 candidates (-53.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1203123
Fresh268
Picked101
Done000
Total1239132

Merged error: 0.1b

Counts
132 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.1b
(/ (cos x) x)
2.5b
(- (/ 1.0 x) (/ (cos x) x))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×*-un-lft-identity times-frac
23×add-cube-cbrt
14×add-exp-log
13×associate-*l*
12×associate-*r*
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×div-inv
5×pow1 add-log-exp
4×frac-times associate-*r/ prod-exp
3×sub-neg flip3-- div-exp associate-/r* frac-sub flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv distribute-rgt-in distribute-rgt-out-- distribute-lft-in cbrt-unprod
1×rec-exp frac-2neg diff-log 1-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 106
Calls
3 calls:
24.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
4.0ms
(/ (cos x) x)
14.0ms
(- (/ 1.0 x) (/ (cos x) x))

series30.0ms

Counts
3 → 9
Calls
3 calls:
12.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
7.0ms
(/ (cos x) x)
11.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify60.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0478762
12181681
25001665

prune132.0ms

Filtered
87 candidates to 115 candidates (-32.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1141115
Fresh178
Picked011
Done000
Total1159124

Merged error: 0.1b

Counts
124 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
0.6b
(* (cbrt x) (cbrt x))
2.3b
(- 1.0 (cos x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×cbrt-prod
16×*-un-lft-identity
14×add-cube-cbrt
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* add-log-exp
4×add-cbrt-cube unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 76
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
6.0ms
(* (cbrt x) (cbrt x))
4.0ms
(- 1.0 (cos x))

series76.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(cbrt x)
23.0ms
(cbrt x)
26.0ms
(* (cbrt x) (cbrt x))
3.0ms
(- 1.0 (cos x))

simplify101.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0232374
1716346
23159300
35001287

prune74.0ms

Filtered
58 candidates to 88 candidates (-51.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh077
Picked011
Done011
Total88997

Merged error: 0.1b

Counts
97 → 9

regimes115.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch46.0ms

Steps
ItersRangePoint
9
7.645058104590196e-05
788.3067460884123
0.038605668716545485
10
-3059576083.432367
-1.5381061282256278e-05
-0.031423183130095615

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03617
13617

end0.0ms

analyze222.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14

sample1.8s

Algorithm
intervals
Results
863.0ms1645×body2560valid
337.0ms1226×body1280valid
254.0ms1492×body640valid
126.0ms927×body320valid
92.0ms2224×body80valid
41.0ms486×body160valid

Profiling

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