Details

Time bar (total: 6.8s)

sample144.0ms

Algorithm
intervals
Results
72.0ms56×body2560valid
41.0ms91×body1280valid
14.0ms59×body640valid
4.0ms24×body320valid
1.0ms14×body160valid
1.0ms12×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

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: 31.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.9b
(- 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))

series46.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (- 1.0 (cos x)) (sin x))
13.0ms
(- 1.0 (cos x))

simplify75.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0217394
1620370
22465369
35002369

prune230.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New411758
Fresh000
Picked101
Done000
Total421759

Merged error: 0.7b

Counts
59 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.3b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×associate-*r*
3×pow-unpow associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 92
Calls
4 calls:
6.0ms
(* (cos x) (+ (cos x) 1.0))
4.0ms
(+ (cos x) 1.0)
3.0ms
(pow (cos x) 3)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series97.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (cos x) (+ (cos x) 1.0))
8.0ms
(+ (cos x) 1.0)
24.0ms
(pow (cos x) 3)
41.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify73.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0347592
11725554
25002534

prune341.0ms

Filtered
104 candidates to 61 candidates (58.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New986104
Fresh31316
Picked101
Done000
Total10219121

Merged error: 0.7b

Counts
121 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
0.4b
(pow (pow (cos x) 3) 3)
1.7b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
56×unpow-prod-down cube-prod
44×difference-of-squares
40×cbrt-prod
27×sqr-pow
18×*-un-lft-identity
14×add-cube-cbrt
8×add-log-exp
7×add-exp-log
6×pow-unpow add-cbrt-cube
5×pow1 pow-exp
4×cube-mult unpow3
3×pow-to-exp
2×pow-pow rem-cube-cbrt
1×+-commutative sub-neg flip3-- flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 135
Calls
4 calls:
4.0ms
(+ (cos x) 1.0)
2.0ms
(pow (cos x) 3)
5.0ms
(pow (pow (cos x) 3) 3)
25.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series122.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(+ (cos x) 1.0)
24.0ms
(pow (cos x) 3)
52.0ms
(pow (pow (cos x) 3) 3)
38.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify64.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04141013
11536952
25001915

prune376.0ms

Filtered
147 candidates to 60 candidates (40.8%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1425147
Fresh41418
Picked101
Done000
Total14719166

Merged error: 0.6b

Counts
166 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (pow (cos x) 9))
0.3b
(+ (cos x) 1.0)
0.8b
(pow (cos x) 9)
1.7b
(- (pow 1.0 3) (cbrt (pow (cos x) 9)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
19×cbrt-prod
16×difference-of-squares
14×unpow-prod-down
12×*-un-lft-identity
10×sqr-pow
8×add-cube-cbrt add-log-exp
5×pow1 add-exp-log
4×cube-prod add-cbrt-cube
3×pow-unpow
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ pow1/3 diff-log pow-exp sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 73
Calls
4 calls:
2.0ms
(cbrt (pow (cos x) 9))
7.0ms
(+ (cos x) 1.0)
2.0ms
(pow (cos x) 9)
10.0ms
(- (pow 1.0 3) (cbrt (pow (cos x) 9)))

series121.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(cbrt (pow (cos x) 9))
8.0ms
(+ (cos x) 1.0)
51.0ms
(pow (cos x) 9)
37.0ms
(- (pow 1.0 3) (cbrt (pow (cos x) 9)))

simplify117.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0301562
1959544
23732543
35001541

prune305.0ms

Filtered
85 candidates to 62 candidates (72.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New82385
Fresh21618
Picked101
Done000
Total8519104

Merged error: 0.6b

Counts
104 → 19

regimes275.0ms

Accuracy

98.4% (0.5b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 30.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04239
14239

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.2s1633×body2560valid
1.2s2748×body1280valid
432.0ms1874×body640valid
153.0ms930×body320valid
50.0ms460×body160valid
23.0ms353×body80valid
8.0ms2×body5120valid

Profiling

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