Details

Time bar (total: 6.8s)

analyze520.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
37.5%62.5%0%4
43.7%56.2%0%5
46.9%53.1%0%6
48.4%51.5%0%7
49.2%50.8%0%8
49.6%50.4%0%9
49.8%50.2%0%10
49.9%50.1%0%11
49.9%50%0%12
50%50%0%13
50%49.9%0%14

sample132.0ms

Algorithm
intervals
Results
59.0ms40×body2560valid
38.0ms84×body1280valid
18.0ms75×body640valid
6.0ms32×body320valid
1.0ms11×body160valid
1.0ms14×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
02297
12297

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.2b
(- 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 → 51
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))
4.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
05058605

prune137.0ms

Filtered
42 candidates to 57 candidates (-35.7%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New401757
Fresh000
Picked101
Done000
Total411758

Merged error: 0.3b

Counts
58 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ 1.0 (cos x)))
0.4b
(+ 1.0 (cos x))
0.4b
(pow (cos x) 3)
2.0b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite26.0ms

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 → 91
Calls
4 calls:
6.0ms
(* (cos x) (+ 1.0 (cos x)))
4.0ms
(+ 1.0 (cos x))
2.0ms
(pow (cos x) 3)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series20.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* (cos x) (+ 1.0 (cos x)))
2.0ms
(+ 1.0 (cos x))
6.0ms
(pow (cos x) 3)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
05011963

prune196.0ms

Filtered
61 candidates to 103 candidates (-68.9%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New976103
Fresh21416
Picked101
Done000
Total10020120

Merged error: 0.2b

Counts
120 → 20

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(pow (cos x) 3)
0.7b
(pow (cos x) 6)
1.8b
(- (pow (pow 1.0 3) 3) (pow (pow (cos x) 3) 3))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
165×unpow-prod-down
162×cube-prod
152×add-sqr-sqrt
100×difference-of-squares
63×sqr-pow
54×*-un-lft-identity
21×distribute-lft-out--
12×add-cube-cbrt
9×pow-unpow
7×pow1 add-exp-log
6×add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow pow-exp
2×cube-mult unpow3 rem-cube-cbrt
1×difference-cubes sub-neg flip3-- diff-log flip--
Counts
4 → 196
Calls
4 calls:
2.0ms
(pow (cos x) 3)
2.0ms
(pow (cos x) 3)
2.0ms
(pow (cos x) 6)
40.0ms
(- (pow (pow 1.0 3) 3) (pow (pow (cos x) 3) 3))

series27.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos x) 3)
5.0ms
(pow (cos x) 3)
7.0ms
(pow (cos x) 6)
12.0ms
(- (pow (pow 1.0 3) 3) (pow (pow (cos x) 3) 3))

simplify74.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049503473
149503473

prune394.0ms

Filtered
72 candidates to 208 candidates (-188.9%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New2044208
Fresh21719
Picked101
Done000
Total20721228

Merged error: 0.2b

Counts
228 → 21

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(/ (sin x) (- 1.0 (cos x)))
2.2b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
105×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 158
Calls
3 calls:
8.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms
(/ (sin x) (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series18.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
8.0ms
(/ (sin x) (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

simplify60.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050932252

prune144.0ms

Filtered
98 candidates to 167 candidates (-70.4%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New1625167
Fresh41620
Picked101
Done000
Total16721188

Merged error: 0.2b

Counts
188 → 21

regimes262.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07384
17384

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.2s1542×body2560valid
1.4s2773×body1280valid
504.0ms1923×body640valid
169.0ms921×body320valid
59.0ms480×body160valid
26.0ms355×body80valid
18.0ms6×body5120valid

Profiling

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