Details

Time bar (total: 4.6s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1

sample103.0ms

Algorithm
intervals
Results
57.0ms141×body1280valid
18.0ms21×body2560valid
15.0ms68×body640valid
3.0ms18×body320valid
1.0ms6×body160valid
0.0ms2×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.7b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b
(- (cos (+ x eps)) (cos x))
2.6b
(cos (+ x eps))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 23
Calls
2 calls:
6.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series15.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

simplify24.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
04999270
14999270

prune59.0ms

Filtered
23 candidates to 29 candidates (-26.1%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New23629
Fresh000
Picked101
Done000
Total24630

Merged error: 0.3b

Counts
30 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b
(+ x (+ x eps))
0.3b
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.8b
(sin (/ (+ x (+ x eps)) 2))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×sum-log distribute-lft-out
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 60
Calls
4 calls:
11.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
8.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

series36.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms
(+ x (+ x eps))
12.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04907890
14907890

prune148.0ms

Filtered
53 candidates to 72 candidates (-35.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New65772
Fresh145
Picked011
Done000
Total661278

Merged error: 0.3b

Counts
78 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b
(sin (/ (+ x (+ x eps)) 2))
5.2b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.2b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.2b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod cbrt-div pow1/3 sin-mult
Counts
4 → 37
Calls
4 calls:
7.0ms
(sin (/ (+ x (+ x eps)) 2))
8.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
8.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
8.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

series96.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sin (/ (+ x (+ x eps)) 2))
29.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
29.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
32.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify49.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
05057721

prune222.0ms

Filtered
45 candidates to 49 candidates (-8.9%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New47249
Fresh01010
Picked011
Done011
Total471461

Merged error: 0.2b

Counts
61 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

2.8b
(sin (/ (+ x (+ x eps)) 2))
2.8b
(sin (/ (+ x (+ x eps)) 2))
5.2b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.2b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×cbrt-prod cbrt-div pow1/3 sin-mult
Counts
4 → 34
Calls
4 calls:
7.0ms
(sin (/ (+ x (+ x eps)) 2))
7.0ms
(sin (/ (+ x (+ x eps)) 2))
8.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
9.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

series72.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sin (/ (+ x (+ x eps)) 2))
6.0ms
(sin (/ (+ x (+ x eps)) 2))
31.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
29.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify47.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05057610

prune170.0ms

Filtered
42 candidates to 46 candidates (-9.5%)
Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New46046
Fresh01111
Picked011
Done022
Total461460

Merged error: 0.2b

Counts
60 → 14

regimes240.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.9b

bsearch50.0ms

Steps
ItersRangePoint
5
0.3430950014596435
1.2592990190863729
0.3504657788551427
9
-117615.3612092743
-0.00010668323082749249
-0.0004184201223143189

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06938
16938

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s4442×body1280valid
574.0ms636×body2560valid
440.0ms1879×body640valid
110.0ms690×body320valid
35.0ms277×body160valid
4.0ms76×body80valid

Profiling

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