Details

Time bar (total: 2.8s)

sample58.0ms

Algorithm
intervals
Results
27.0ms57×body2560valid
9.0ms55×body640valid
7.0ms31×body1280valid
3.0ms73×body80valid
3.0ms25×body320valid
1.0ms15×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
16.4b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

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:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

series14.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
10.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify58.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune88.0ms

Filtered
34 candidates to 48 candidates (-41.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New39948
Fresh000
Picked101
Done000
Total40949

Merged error: 0.2b

Counts
49 → 9

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))
2.0b
(- 1.0 (cos x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 114
Calls
3 calls:
5.0ms
(/ (- 1.0 (cos x)) x)
15.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

series13.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (- 1.0 (cos x)) x)
5.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

simplify59.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0521814
12334726
25003690

prune145.0ms

Filtered
81 candidates to 123 candidates (-51.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1185123
Fresh268
Picked101
Done000
Total12111132

Merged error: 0.2b

Counts
132 → 11

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.1b
(/ (cos x) x)
2.0b
(- (/ 1.0 x) (/ (cos x) x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×*-un-lft-identity times-frac
23×add-cube-cbrt
14×add-exp-log
13×associate-*l*
12×associate-*r*
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×div-inv
5×pow1 add-log-exp
4×frac-times associate-*r/ prod-exp
3×sub-neg flip3-- div-exp associate-/r* frac-sub flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv distribute-rgt-in distribute-rgt-out-- distribute-lft-in cbrt-unprod
1×rec-exp frac-2neg diff-log 1-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 106
Calls
3 calls:
19.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
3.0ms
(/ (cos x) x)
12.0ms
(- (/ 1.0 x) (/ (cos x) x))

series21.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
3.0ms
(/ (cos x) x)
6.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify59.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0478762
12181681
25001665

prune144.0ms

Filtered
87 candidates to 115 candidates (-32.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1123115
Fresh2810
Picked101
Done000
Total11511126

Merged error: 0.2b

Counts
126 → 11

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (- (/ 1.0 x) (* (cos x) (/ 1 x))))
0.2b
(* (cos x) (/ 1 x))
2.0b
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
22×times-frac
21×add-exp-log *-un-lft-identity
19×add-cube-cbrt
17×associate-*r*
16×associate-*l*
13×associate-*r/ add-cbrt-cube
8×prod-exp
7×pow1 un-div-inv
6×frac-times frac-sub sub-div unswap-sqr
5×add-log-exp
4×div-exp cbrt-unprod div-inv
3×sub-neg flip3-- flip--
2×cbrt-undiv distribute-rgt-in rec-exp distribute-rgt-out-- distribute-lft-in 1-exp pow-prod-down *-commutative
1×diff-log associate-*l/
Counts
3 → 105
Calls
3 calls:
14.0ms
(* (/ 1 x) (- (/ 1.0 x) (* (cos x) (/ 1 x))))
7.0ms
(* (cos x) (/ 1 x))
6.0ms
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

series19.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(* (/ 1 x) (- (/ 1.0 x) (* (cos x) (/ 1 x))))
3.0ms
(* (cos x) (/ 1 x))
6.0ms
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

simplify61.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0486805
12335646
25001614

prune107.0ms

Filtered
76 candidates to 114 candidates (-50.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1140114
Fresh01010
Picked011
Done000
Total11411125

Merged error: 0.2b

Counts
125 → 11

regimes69.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.3b

bsearch27.0ms

Steps
ItersRangePoint
9
1.7854326419021657e-07
0.0364262917160445
0.03373038231043822
8
-442.47528987694835
-0.030191044061917315
-0.03671056288763298

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03613
13613

end0.0ms

sample1.8s

Algorithm
intervals
Results
795.0ms1667×body2560valid
330.0ms1293×body1280valid
227.0ms1423×body640valid
107.0ms899×body320valid
81.0ms2235×body80valid
38.0ms483×body160valid

Profiling

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