Details

Time bar (total: 3.3s)

analyze234.0ms

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

sample58.0ms

Algorithm
intervals
Results
25.0ms44×body2560valid
11.0ms42×body1280valid
7.0ms45×body640valid
3.0ms92×body80valid
2.0ms19×body320valid
1.0ms14×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
05008
15008

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.0b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b
(- 1.0 (cos x))
13.2b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
add-exp-log add-cbrt-cube
times-frac associate-/l*
add-cube-cbrt add-log-exp
distribute-lft-out-- difference-of-squares
pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 41
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))

simplify46.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04894437
14894437

prune117.0ms

Filtered
34 candidates to 47 candidates (-38.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New39847
Fresh000
Picked101
Done000
Total40848

Merged error: 0.1b

Counts
48 → 8

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
1.8b
(- 1.0 (cos x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
103×add-sqr-sqrt *-un-lft-identity
69×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
associate-/r* div-inv
add-log-exp
cbrt-undiv div-exp
pow1 div-sub associate-/l/
flip3-- frac-2neg clear-num flip--
sub-neg diff-log
Counts
3 → 146
Calls
3 calls:
8.0ms
(/ (/ (- 1.0 (cos x)) x) x)
5.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series14.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (/ (- 1.0 (cos x)) x) x)
5.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

simplify58.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
054811984

prune168.0ms

Filtered
101 candidates to 155 candidates (-53.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1523155
Fresh257
Picked011
Done000
Total1549163

Merged error: 0.1b

Counts
163 → 9

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.9b
(- (/ 1.0 x) (/ (cos x) x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
95×times-frac
78×*-un-lft-identity
38×add-cube-cbrt
20×distribute-lft-out-- difference-of-squares
15×associate-/l*
12×div-inv
add-exp-log add-cbrt-cube
associate-/r*
distribute-rgt-out-- add-log-exp
associate-/l/
pow1
cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
sub-neg diff-log div-sub
Counts
3 → 117
Calls
3 calls:
15.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
3.0ms
(/ (cos x) x)
15.0ms
(- (/ 1.0 x) (/ (cos x) x))

series20.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms
(/ (cos x) x)
6.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
051741525

prune151.0ms

Filtered
96 candidates to 126 candidates (-31.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1233126
Fresh257
Picked101
Done011
Total1269135

Merged error: 0.1b

Counts
135 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
1.8b
(- 1.0 (cos x))
1.8b
(- 1.0 (cos x))
1.8b
(- 1.0 (cos x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×*-un-lft-identity
28×cbrt-prod
12×add-cube-cbrt cbrt-div
11×pow1
10×swap-sqr add-log-exp
flip3-- flip-- distribute-lft-out--
associate-*r* associate-*l*
difference-of-squares
add-exp-log pow1/3
frac-times add-cbrt-cube unswap-sqr
sub-neg diff-log
associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
10.0ms
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series37.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

simplify37.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
051281093

prune170.0ms

Filtered
72 candidates to 107 candidates (-48.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1061107
Fresh167
Picked101
Done011
Total1088116

Merged error: 0.1b

Counts
116 → 8

regimes61.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch30.0ms

Steps
ItersRangePoint
9
4.731074194027232e-05
8.557275288284076
0.02020093954594806
10
-253.3258898344875
-2.6527926053742094e-15
-0.030208352135472436

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04030
14030

end0.0ms

sample1.9s

Algorithm
intervals
Results
856.0ms1607×body2560valid
375.0ms1287×body1280valid
262.0ms1496×body640valid
113.0ms869×body320valid
84.0ms2256×body80valid
42.0ms485×body160valid

Profiling

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