Details

Time bar (total: 4.3s)

sample58.0ms

Algorithm
intervals
Results
23.0ms52×body2560valid
9.0ms38×body1280valid
8.0ms53×body640valid
5.0ms43×body320valid
2.0ms58×body80valid
1.0ms12×body160valid

simplify7.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.9b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
16.3b
(/ (- 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))

series81.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- 1.0 (cos x))
59.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune143.0ms

Filtered
48 candidates to 34 candidates (29.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/720 (pow x 4)) 1/2)
0.1b
(* 1/720 (pow x 4))
0.4b
(* 1/24 (pow x 2))
9.8b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×associate-*r*
14×add-exp-log
11×add-log-exp
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 sqr-pow
2×pow-to-exp diff-log pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+
Counts
4 → 77
Calls
4 calls:
4.0ms
(+ (* 1/720 (pow x 4)) 1/2)
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(+ (* 1/720 (pow x 4)) 1/2)
45.0ms
(* 1/720 (pow x 4))
29.0ms
(* 1/24 (pow x 2))
55.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0312425
11388378
25002370

prune285.0ms

Filtered
89 candidates to 56 candidates (37.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New89089
Fresh099
Picked011
Done000
Total891099

Merged error: 0.1b

Counts
99 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.5b
(- 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:
13.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
8.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series132.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
56.0ms
(/ (- 1.0 (cos x)) x)
22.0ms
(- 1.0 (cos x))

simplify62.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0521814
12334726
25001690

prune412.0ms

Filtered
123 candidates to 80 candidates (35.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1167123
Fresh448
Picked101
Done011
Total12112133

Merged error: 0.1b

Counts
133 → 12

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(/ (sqrt (- 1.0 (cos x))) x)
1.5b
(- 1.0 (cos x))
1.5b
(- 1.0 (cos x))

rewrite23.0ms

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)
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series270.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (sqrt (- 1.0 (cos x))) x)
109.0ms
(/ (sqrt (- 1.0 (cos x))) x)
22.0ms
(- 1.0 (cos x))
26.0ms
(- 1.0 (cos x))

simplify101.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02421020
1706972
22954960
35002960

prune410.0ms

Filtered
138 candidates to 92 candidates (33.3%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1335138
Fresh2810
Picked101
Done011
Total13614150

Merged error: 0.1b

Counts
150 → 14

regimes98.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch80.0ms

Steps
ItersRangePoint
8
3.9971791970784e-05
0.9384348231062936
0.03517186928626813
7
-0.04031575958609914
-0.0011811564698516964
-0.027410308857751114

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04232
14232

end0.0ms

sample1.7s

Algorithm
intervals
Results
771.0ms1622×body2560valid
295.0ms1202×body1280valid
234.0ms1488×body640valid
104.0ms951×body320valid
74.0ms2266×body80valid
37.0ms471×body160valid

Profiling

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