Details

Time bar (total: 3.6s)

sample53.0ms

Algorithm
intervals
Results
23.0ms51×body2560valid
11.0ms48×body1280valid
6.0ms42×body640valid
3.0ms74×body80valid
2.0ms24×body320valid
1.0ms17×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 (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize6.0ms

Local error

Found 2 expressions with local error:

1.6b
(- 1.0 (cos x))
16.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
2.0ms
(- 1.0 (cos x))
8.0ms
(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35001239

prune110.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
1.6b
(- 1.0 (cos x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
103×add-sqr-sqrt *-un-lft-identity
69×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 147
Calls
3 calls:
11.0ms
(/ (/ (- 1.0 (cos x)) x) x)
7.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series111.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ (/ (- 1.0 (cos x)) x) x)
41.0ms
(/ (- 1.0 (cos x)) x)
23.0ms
(- 1.0 (cos x))

simplify50.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05311270
118991197
250011186

prune281.0ms

Filtered
156 candidates to 104 candidates (66.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.6b
(- (/ 1.0 x) (/ (cos x) x))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
95×times-frac
78×*-un-lft-identity
38×add-cube-cbrt
20×distribute-lft-out-- difference-of-squares
15×associate-/l*
12×div-inv
7×add-exp-log add-cbrt-cube
6×associate-/r*
5×distribute-rgt-out-- add-log-exp
4×associate-/l/
3×pow1
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
1×sub-neg diff-log div-sub
Counts
3 → 118
Calls
3 calls:
46.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
3.0ms
(/ (cos x) x)
16.0ms
(- (/ 1.0 x) (/ (cos x) x))

series186.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
29.0ms
(/ (cos x) x)
60.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify45.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04631015
11518940
25001936

prune283.0ms

Filtered
127 candidates to 100 candidates (78.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
0.2b
(* (cos x) (/ 1 x))
1.6b
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
23×times-frac
21×*-un-lft-identity
20×add-cube-cbrt
14×add-exp-log
13×associate-*r*
10×add-cbrt-cube
7×div-inv
6×associate-/l/
5×pow1 distribute-rgt-out-- associate-*r/ un-div-inv add-log-exp
4×prod-exp frac-sub associate-/l* sub-div
3×div-exp associate-*l* associate-/r* unswap-sqr
2×cbrt-undiv flip3-- flip-- cbrt-unprod
1×sub-neg rec-exp frac-2neg diff-log 1-exp div-sub pow-prod-down clear-num *-commutative
Counts
3 → 91
Calls
3 calls:
22.0ms
(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
11.0ms
(* (cos x) (/ 1 x))
10.0ms
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

series188.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
29.0ms
(* (cos x) (/ 1 x))
60.0ms
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0432678
11826583
25001560

prune191.0ms

Filtered
100 candidates to 75 candidates (75.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.1b

bsearch70.0ms

Steps
ItersRangePoint
9
7.206039552426127e-07
5.540917366542361
0.029021184668687444
10
-204248214.92732975
-1.534026600097144e-05
-0.034943047385034086

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03718
13718

end0.0ms

sample1.6s

Algorithm
intervals
Results
761.0ms1594×body2560valid
304.0ms1300×body1280valid
213.0ms1457×body640valid
98.0ms914×body320valid
71.0ms2210×body80valid
40.0ms525×body160valid