Details

Time bar (total: 3.4s)

sample51.0ms

Algorithm
intervals
Results
20.0ms48×body2560valid
10.0ms46×body1280valid
7.0ms48×body640valid
4.0ms36×body320valid
3.0ms70×body80valid
1.0ms8×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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
15.5b
(/ (- 1.0 (cos x)) (* x x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
82×*-un-lft-identity
75×times-frac
48×add-cube-cbrt
18×swap-sqr associate-*r* associate-*l*
17×distribute-lft-out-- difference-of-squares
15×associate-/r*
7×add-exp-log add-cbrt-cube
6×*-commutative unswap-sqr
5×associate-/l*
4×add-log-exp
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num cbrt-unprod div-inv
Counts
2 → 126
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
11.0ms
(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
49.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify57.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04871050
119611000
25002981

prune187.0ms

Filtered
132 candidates to 73 candidates (44.7%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11814132
Fresh000
Picked101
Done000
Total11914133

Merged error: 0.2b

Counts
133 → 14

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.8b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
25×*-un-lft-identity
15×associate-*r*
13×add-exp-log
11×associate-*l* unswap-sqr
9×add-cube-cbrt unpow-prod-down
8×add-log-exp
7×pow1 add-cbrt-cube
6×prod-exp distribute-lft-out--
5×difference-of-squares sqr-pow
4×distribute-lft-out
3×unpow2
2×pow-to-exp diff-log pow-prod-down pow-exp associate--l+ *-commutative cbrt-unprod
1×+-commutative sub-neg flip3-- sum-log flip--
Counts
3 → 80
Calls
3 calls:
6.0ms
(* 1/720 (pow x 4))
6.0ms
(* 1/24 (pow x 2))
24.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series108.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 1/720 (pow x 4))
29.0ms
(* 1/24 (pow x 2))
43.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0292472
11147437
25002433

prune150.0ms

Filtered
89 candidates to 50 candidates (43.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New88189
Fresh11213
Picked101
Done000
Total9013103

Merged error: 0.2b

Counts
103 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.8b
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
11×associate-*l*
9×add-cube-cbrt
8×unpow-prod-down add-log-exp
7×pow1 add-cbrt-cube unswap-sqr
6×prod-exp distribute-lft-out
4×distribute-lft-out-- sqr-pow
2×pow-to-exp associate-+r+ pow-prod-down pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative associate-+r- sub-neg flip3-+ diff-log flip-+
Counts
3 → 75
Calls
3 calls:
6.0ms
(* 1/720 (pow x 4))
6.0ms
(* 1/24 (pow x 2))
26.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series108.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 1/720 (pow x 4))
29.0ms
(* 1/24 (pow x 2))
43.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify38.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0270385
11090354
25002354

prune140.0ms

Filtered
84 candidates to 47 candidates (44.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh01212
Picked011
Done000
Total841397

Merged error: 0.2b

Counts
97 → 13

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) x)
0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.5b
(- 1.0 (cos x))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt
118×*-un-lft-identity
117×frac-times
99×associate-/l*
77×add-cube-cbrt
75×associate-/r*
46×times-frac
27×add-exp-log
26×clear-num
25×frac-2neg
22×associate-/l/
19×associate-*r* distribute-lft-out--
18×difference-of-squares
17×add-cbrt-cube
13×associate-*r/ associate-*l*
12×flip3-- flip--
9×div-exp associate-*l/
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv add-log-exp
4×cbrt-unprod
3×un-div-inv div-inv
2×rec-exp 1-exp
1×sub-neg diff-log div-sub pow-prod-down *-commutative
Counts
3 → 253
Calls
3 calls:
6.0ms
(/ (- 1.0 (cos x)) x)
22.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
4.0ms
(- 1.0 (cos x))

series110.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(/ (- 1.0 (cos x)) x)
48.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
19.0ms
(- 1.0 (cos x))

simplify52.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010621940
150011773

prune402.0ms

Filtered
262 candidates to 135 candidates (48.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2548262
Fresh8311
Picked101
Done011
Total26312275

Merged error: 0.2b

Counts
275 → 12

regimes51.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch56.0ms

Steps
ItersRangePoint
9
0.0004381094517774334
96283.49646244562
0.03411142251183559
6
-0.04448272872103196
-0.010589856477353462
-0.03054575583888737

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03613
13613

end0.0ms

sample1.6s

Algorithm
intervals
Results
751.0ms1597×body2560valid
290.0ms1226×body1280valid
237.0ms1534×body640valid
103.0ms913×body320valid
73.0ms2240×body80valid
41.0ms490×body160valid