Details

Time bar (total: 5.4s)

sample106.0ms

Algorithm
intervals
Results
44.0ms55×body2560valid
15.0ms34×body1280valid
13.0ms47×body640valid
5.0ms83×body80valid
5.0ms26×body320valid
1.0ms11×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05008
15008

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.7b

Counts
2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
15.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite19.0ms

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:
6.0ms
(- 1.0 (cos x))
11.0ms
(/ (- 1.0 (cos x)) (* x x))

series14.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(- 1.0 (cos x))
10.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify81.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
04894440
14894440

prune170.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (cos x))) x)
0.2b
(/ (sqrt (- 1.0 (cos x))) x)
2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))

rewrite38.0ms

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:
12.0ms
(/ (sqrt (- 1.0 (cos x))) x)
11.0ms
(/ (sqrt (- 1.0 (cos x))) x)
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series43.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (sqrt (- 1.0 (cos x))) x)
16.0ms
(/ (sqrt (- 1.0 (cos x))) x)
5.0ms
(- 1.0 (cos x))
5.0ms
(- 1.0 (cos x))

simplify82.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049801530
149801530

prune423.0ms

Filtered
92 candidates to 138 candidates (-50.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1344138
Fresh279
Picked101
Done000
Total13711148

Merged error: 0.1b

Counts
148 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))
2.1b
(log (exp (- 1.0 (cos x))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt *-un-lft-identity
36×times-frac sqrt-prod
31×add-cube-cbrt
30×log-pow
25×exp-prod
12×associate-/l*
9×pow1
8×add-log-exp
7×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
5×log-prod
3×sub-neg associate-/r*
2×flip3-- diff-log exp-sum flip--
1×cbrt-undiv log-div frac-2neg exp-diff div-exp rem-log-exp clear-num div-inv
Counts
4 → 111
Calls
4 calls:
17.0ms
(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
7.0ms
(- 1.0 (cos x))
7.0ms
(- 1.0 (cos x))
9.0ms
(log (exp (- 1.0 (cos x))))

series33.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
5.0ms
(- 1.0 (cos x))
5.0ms
(- 1.0 (cos x))
6.0ms
(log (exp (- 1.0 (cos x))))

simplify82.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
053101206

prune415.0ms

Filtered
80 candidates to 123 candidates (-53.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1194123
Fresh2810
Picked101
Done000
Total12212134

Merged error: 0.1b

Counts
134 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))
2.1b
(log (exp (- 1.0 (cos x))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
6×add-cube-cbrt log-pow
5×pow1 log-prod exp-prod
4×add-exp-log sub-neg add-cbrt-cube distribute-lft-out-- difference-of-squares
3×flip3-- diff-log flip--
2×exp-sum
1×log-div exp-diff rem-log-exp
Counts
4 → 62
Calls
4 calls:
7.0ms
(- 1.0 (cos x))
7.0ms
(- 1.0 (cos x))
7.0ms
(- 1.0 (cos x))
9.0ms
(log (exp (- 1.0 (cos x))))

series20.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(- 1.0 (cos x))
5.0ms
(- 1.0 (cos x))
5.0ms
(- 1.0 (cos x))
6.0ms
(log (exp (- 1.0 (cos x))))

simplify72.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
04903520
14903520

prune264.0ms

Filtered
52 candidates to 74 candidates (-42.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New72274
Fresh2911
Picked011
Done000
Total741286

Merged error: 0.1b

Counts
86 → 12

regimes158.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.4b

bsearch45.0ms

Steps
ItersRangePoint
10
0.01683730658649282
12785707414306.22
0.03002211543800249
10
-0.2101619750885166
-2.51237587459879e-12
-0.03140225698466425

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07070
17070

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.4s1668×body2560valid
592.0ms1277×body1280valid
436.0ms1444×body640valid
201.0ms944×body320valid
139.0ms2194×body80valid
67.0ms473×body160valid

Profiling

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