Details

Time bar (total: 5.0s)

sample105.0ms

Algorithm
intervals
Results
38.0ms95×body1280valid
28.0ms21×body2560valid
16.0ms73×body640valid
10.0ms37×body320valid
2.0ms15×body160valid
1.0ms15×body80valid

simplify7.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.1b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (- 1.0 (cos x)) (sin x))
1.0b
(- 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))

series10.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

simplify80.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune130.0ms

Filtered
58 candidates to 42 candidates (27.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New411758
Fresh000
Picked101
Done000
Total421759

Merged error: 0.3b

Counts
59 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (+ (cos x) 1.0))
0.5b
(pow (cos x) 3)
0.7b
(+ (cos x) 1.0)
0.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite27.0ms

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))
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
12.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series18.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (cos x) (+ (cos x) 1.0))
5.0ms
(pow (cos x) 3)
2.0ms
(+ (cos x) 1.0)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify70.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0353611
11730571
25001567

prune193.0ms

Filtered
104 candidates to 61 candidates (41.3%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New968104
Fresh51116
Picked101
Done000
Total10219121

Merged error: 0.2b

Counts
121 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cos x) 3)
0.7b
(+ (cos x) 1.0)
0.7b
(- (pow 1.0 3) (pow (cos x) 3))
1.5b
(log (- (pow 1.0 3) (pow (cos x) 3)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
32×difference-of-squares
30×*-un-lft-identity
27×unpow-prod-down cube-prod
25×log-prod
17×sqr-pow
10×distribute-lft-out--
8×add-cube-cbrt add-log-exp
6×pow1 add-exp-log
5×add-cbrt-cube
3×pow-unpow
2×difference-cubes log-div flip3-- flip--
1×+-commutative cube-mult pow-to-exp sub-neg pow-pow flip3-+ diff-log unpow3 rem-log-exp pow-exp sum-log log-pow flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 105
Calls
4 calls:
2.0ms
(pow (cos x) 3)
6.0ms
(+ (cos x) 1.0)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))
11.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))

series33.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos x) 3)
2.0ms
(+ (cos x) 1.0)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))
19.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))

simplify50.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0338848
11210805
25002769

prune244.0ms

Filtered
117 candidates to 63 candidates (46.2%)
Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New1134117
Fresh11718
Picked011
Done000
Total11422136

Merged error: 0.2b

Counts
136 → 22

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (cos x) 1.0)
0.7b
(+ (cos x) 1.0)
0.7b
(+ (cos x) 1.0)
0.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
20×*-un-lft-identity
16×difference-of-squares
12×unpow-prod-down cube-prod add-log-exp
8×sqr-pow
5×distribute-lft-out--
4×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
1×difference-cubes sub-neg flip3-- diff-log flip--
Counts
4 → 70
Calls
4 calls:
4.0ms
(+ (cos x) 1.0)
4.0ms
(+ (cos x) 1.0)
4.0ms
(+ (cos x) 1.0)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series13.0ms

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

simplify97.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0224492
1681468
22962468
35002468

prune170.0ms

Filtered
82 candidates to 56 candidates (31.7%)
Pruning

21 alts after pruning (20 fresh and 1 done)

PrunedKeptTotal
New81182
Fresh11920
Picked101
Done011
Total8321104

Merged error: 0.2b

Counts
104 → 21

regimes248.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 16.4b

bsearch60.0ms

Steps
ItersRangePoint
7
0.012859339055769341
0.3555464171021314
0.020879752328029882
15
-5.198581744599781
1.0450147493914085e-304
-0.02324761303887589

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04528
14528

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s2865×body1280valid
1.1s835×body2560valid
508.0ms2140×body640valid
175.0ms1102×body320valid
65.0ms588×body160valid
31.0ms469×body80valid
5.0ms1×body5120valid

Profiling

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