Details

Time bar (total: 9.2s)

analyze1.6s

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 50.15564%

sample149.0ms

Algorithm
intervals
Results
79.0ms53×body2560valid
42.0ms90×body1280valid
11.0ms45×body640valid
6.0ms33×body320valid
2.0ms19×body160valid
1.0ms16×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 1.0 (cos x))

rewrite14.0ms

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:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series21.0ms

Counts
2 → 6
Calls
2 calls:
15.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(- 1.0 (cos x))

simplify82.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune123.0ms

Filtered
42 candidates to 58 candidates (-38.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New431558
Fresh000
Picked101
Done000
Total441559

Merged error: 0.1b

Counts
59 → 15

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (sin x) (- 1.0 (cos x)))
0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
2.0b
(- 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 → 159
Calls
3 calls:
6.0ms
(/ (sin x) (- 1.0 (cos x)))
9.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
4.0ms
(- 1.0 (cos x))

series21.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(/ (sin x) (- 1.0 (cos x)))
7.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

simplify62.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05101593
123961450
250021337

prune165.0ms

Filtered
83 candidates to 168 candidates (-102.4%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New1626168
Fresh31114
Picked011
Done000
Total16518183

Merged error: 0.1b

Counts
183 → 18

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- 1.0 (cos x)))
0.1b
(/ (log (exp (- 1.0 (cos x)))) (sin x))
2.0b
(- 1.0 (cos x))
2.1b
(log (exp (- 1.0 (cos x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
30×exp-prod log-pow
27×times-frac
25×add-cube-cbrt
9×pow1 associate-/l* add-log-exp
7×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
5×log-prod
4×exp-sum
3×sub-neg exp-diff associate-/r*
2×log-div diff-log rem-exp-log
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp rem-log-exp clear-num flip-- div-inv
Counts
4 → 103
Calls
4 calls:
5.0ms
(exp (- 1.0 (cos x)))
8.0ms
(/ (log (exp (- 1.0 (cos x)))) (sin x))
3.0ms
(- 1.0 (cos x))
5.0ms
(log (exp (- 1.0 (cos x))))

series21.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(exp (- 1.0 (cos x)))
7.0ms
(/ (log (exp (- 1.0 (cos x)))) (sin x))
3.0ms
(- 1.0 (cos x))
3.0ms
(log (exp (- 1.0 (cos x))))

simplify102.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0295766
1890686
23427674
35001672

prune156.0ms

Filtered
71 candidates to 115 candidates (-62.0%)
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New1141115
Fresh11516
Picked011
Done011
Total11518133

Merged error: 0.1b

Counts
133 → 18

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sin x))
0.2b
(/ (cos x) (sin x))
2.1b
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
28×times-frac
21×add-cube-cbrt
7×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
5×add-log-exp
4×div-inv distribute-lft-out-- difference-of-squares
3×pow1
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 77
Calls
3 calls:
3.0ms
(/ 1.0 (sin x))
4.0ms
(/ (cos x) (sin x))
13.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series26.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ 1.0 (sin x))
6.0ms
(/ (cos x) (sin x))
15.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify59.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0287581
1772552
22215552
35002551

prune80.0ms

Filtered
67 candidates to 86 candidates (-28.4%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New84286
Fresh41115
Picked011
Done112
Total8915104

Merged error: 0.0b

Counts
104 → 15

regimes209.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 30.4b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03327
13327

end0.0ms

analyze1.6s

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 50.15564%

sample4.6s

Algorithm
intervals
Results
2.4s1604×body2560valid
1.3s2761×body1280valid
469.0ms1879×body640valid
149.0ms907×body320valid
58.0ms494×body160valid
24.0ms353×body80valid
6.0ms2×body5120valid

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