Details

Time bar (total: 3.7s)

sample63.0ms

Algorithm
intervals
Results
28.0ms60×body2560valid
10.0ms45×body1280valid
6.0ms41×body640valid
2.0ms24×body320valid
2.0ms72×body80valid
1.0ms14×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.1b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
17.4b
(/ (- 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))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- 1.0 (cos x))
43.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune142.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New40848
Fresh000
Picked011
Done000
Total40949

Merged error: 0.1b

Counts
49 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.6b
(* 1/24 (pow x 2))
12.4b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
6.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series110.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* 1/720 (pow x 4))
25.0ms
(* 1/24 (pow x 2))
49.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268345
11132313
25001307

prune180.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New75075
Fresh077
Picked011
Done011
Total75984

Merged error: 0.1b

Counts
84 → 9

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series226.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (sqrt (- 1.0 (cos x))) x)
92.0ms
(/ (sqrt (- 1.0 (cos x))) x)
22.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify99.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02421020
1706972
22954960
35002960

prune353.0ms

Filtered
138 candidates to 92 candidates (66.7%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1344138
Fresh246
Picked011
Done022
Total13611147

Merged error: 0.0b

Counts
147 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (pow (- 1.0 (cos x)) 3))
0.3b
(pow (- 1.0 (cos x)) 3)
2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
16×cbrt-prod
10×add-cube-cbrt unpow-prod-down cube-prod
8×add-log-exp
6×distribute-lft-out-- difference-of-squares
5×pow1 add-exp-log add-cbrt-cube
4×cube-div flip3-- flip--
3×pow-unpow
2×cube-mult sub-neg cbrt-div diff-log unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 84
Calls
4 calls:
5.0ms
(cbrt (pow (- 1.0 (cos x)) 3))
5.0ms
(pow (- 1.0 (cos x)) 3)
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series105.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cbrt (pow (- 1.0 (cos x)) 3))
49.0ms
(pow (- 1.0 (cos x)) 3)
18.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify35.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0235459
1895444
25002438

prune223.0ms

Filtered
96 candidates to 54 candidates (56.3%)
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New96096
Fresh077
Picked011
Done033
Total9611107

Merged error: 0.0b

Counts
107 → 11

regimes165.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.6b

bsearch77.0ms

Steps
ItersRangePoint
10
1.4708384485510602e-10
911.8039404667869
0.033178106668433634
8
-4.115764337816432
-0.0035716639301171917
-0.033626152411547885

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample1.6s

Algorithm
intervals
Results
769.0ms1658×body2560valid
286.0ms1236×body1280valid
220.0ms1482×body640valid
101.0ms924×body320valid
77.0ms2261×body80valid
36.0ms439×body160valid

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