Details

Time bar (total: 4.5s)

sample51.0ms

Algorithm
intervals
Results
20.0ms41×body2560valid
9.0ms39×body1280valid
7.0ms43×body640valid
3.0ms31×body320valid
3.0ms79×body80valid
2.0ms23×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: 27.8b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.8b
(- 1.0 (cos x))
12.2b
(/ (- 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))

series69.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify64.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune118.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New39948
Fresh000
Picked101
Done000
Total40949

Merged error: 0.1b

Counts
49 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (cos x))) x)
0.2b
(/ (sqrt (- 1.0 (cos x))) x)
2.8b
(- 1.0 (cos x))
2.8b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series224.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (sqrt (- 1.0 (cos x))) x)
95.0ms
(/ (sqrt (- 1.0 (cos x))) x)
18.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify109.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02421020
1706972
22968972
35002972

prune299.0ms

Filtered
138 candidates to 98 candidates (71.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1371138
Fresh178
Picked011
Done000
Total1389147

Merged error: 0.1b

Counts
147 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
2.8b
(- 1.0 (cos x))
2.8b
(- 1.0 (cos x))
2.8b
(- 1.0 (cos x))

rewrite26.0ms

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
9×flip3-- flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log pow1/3
4×frac-times add-cbrt-cube unswap-sqr
3×sub-neg diff-log
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
11.0ms
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series196.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
18.0ms
(- 1.0 (cos x))
22.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify110.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0224813
1704769
23166698
35001681

prune295.0ms

Filtered
110 candidates to 70 candidates (63.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1073110
Fresh257
Picked101
Done011
Total1109119

Merged error: 0.0b

Counts
119 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (sqrt (cbrt (- 1.0 (cos x)))) 4)
2.2b
(log (pow (exp 1) (pow (sqrt (cbrt (- 1.0 (cos x)))) 4)))
2.8b
(- 1.0 (cos x))
2.8b
(- 1.0 (cos x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×unpow-prod-down
10×add-cube-cbrt
8×sqrt-prod add-log-exp
7×log-prod
6×pow1 add-exp-log
5×cbrt-prod
4×pow-pow add-cbrt-cube
3×pow-unpow rem-log-exp distribute-lft-out-- difference-of-squares
2×pow-to-exp sub-neg flip3-- sqrt-pow1 diff-log pow-exp flip-- sqr-pow
1×pow1/2 pow1/3 log-pow sqrt-pow2
Counts
4 → 75
Calls
4 calls:
6.0ms
(pow (sqrt (cbrt (- 1.0 (cos x)))) 4)
3.0ms
(log (pow (exp 1) (pow (sqrt (cbrt (- 1.0 (cos x)))) 4)))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series560.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(pow (sqrt (cbrt (- 1.0 (cos x)))) 4)
354.0ms
(log (pow (exp 1) (pow (sqrt (cbrt (- 1.0 (cos x)))) 4)))
24.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify43.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0301653
1992541
25001513

prune269.0ms

Filtered
87 candidates to 61 candidates (70.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New87087
Fresh077
Picked011
Done011
Total87996

Merged error: 0.0b

Counts
96 → 9

regimes88.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch73.0ms

Steps
ItersRangePoint
10
0.00022027325057658872
62623256.830634765
0.03061966180240735
9
-17.831791951177678
-3.7534567552478157e-06
-0.027340075628349603

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13015

end0.0ms

sample1.8s

Algorithm
intervals
Results
928.0ms1622×body2560valid
303.0ms1231×body1280valid
233.0ms1482×body640valid
124.0ms979×body320valid
83.0ms2213×body80valid
44.0ms473×body160valid

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