Details

Time bar (total: 4.4s)

analyze2.0ms

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

sample98.0ms

Algorithm
intervals
Results
48.0ms137×body1280valid
24.0ms27×body2560valid
13.0ms58×body640valid
3.0ms21×body320valid
1.0ms10×body160valid
0.0ms3×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: 38.7b

Counts
2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (cos (+ x eps)) (cos x))
2.2b
(cos (+ x eps))

rewrite11.0ms

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:
7.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series14.0ms

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

prune60.0ms

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: 0.5b

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)))
2.4b
(sin (/ (+ x (+ x eps)) 2))

rewrite35.0ms

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))))
5.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

series37.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
6.0ms
(+ x (+ x eps))
11.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04907890
14907890

prune153.0ms

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: 0.4b

Counts
78 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))
2.4b
(sin (/ (+ x (+ x eps)) 2))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
Counts
4 → 40
Calls
4 calls:
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
9.0ms
(sin (/ (+ x (+ x eps)) 2))

series59.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(cbrt (sin (/ eps 2)))
18.0ms
(cbrt (sin (/ eps 2)))
18.0ms
(cbrt (sin (/ eps 2)))
6.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify28.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
05501442

prune197.0ms

Filtered
45 candidates to 52 candidates (-15.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New50252
Fresh2810
Picked101
Done011
Total531164

Merged error: 0.4b

Counts
64 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b
(sin (/ (+ x (+ x eps)) 2))
7.1b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
7.1b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
7.1b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite32.0ms

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))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sin (/ (+ x (+ x eps)) 2))
28.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
30.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
28.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05057721

prune181.0ms

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

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New49049
Fresh099
Picked011
Done011
Total491160

Merged error: 0.4b

Counts
60 → 11

regimes197.0ms

Accuracy

95.6% (0.7b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 15.3b

bsearch51.0ms

Steps
ItersRangePoint
6
77961476608.35223
717021154747.934
79663231279.783
5
-2.6358487214306052e-08
-1.0900084561437634e-08
-2.6054432850473577e-08

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06938
16938

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s4452×body1280valid
585.0ms634×body2560valid
424.0ms1857×body640valid
105.0ms671×body320valid
34.0ms296×body160valid
5.0ms90×body80valid

Profiling

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