Details

Time bar (total: 4.4s)

analyze3.0ms

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

sample97.0ms

Algorithm
intervals
Results
42.0ms90×body1280valid
21.0ms22×body2560valid
15.0ms55×body640valid
6.0ms28×body320valid
3.0ms48×body80valid
2.0ms13×body160valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
077
177

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.8b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b
(- (sin (+ x eps)) (sin x))
2.0b
(sin (+ 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 sin-sum add-cbrt-cube
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 23
Calls
2 calls:
6.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series13.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(- (sin (+ x eps)) (sin x))
5.0ms
(sin (+ x eps))

simplify36.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
04933268
14933268

prune48.0ms

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

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New26329
Fresh000
Picked101
Done000
Total27330

Merged error: 0.3b

Counts
30 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (+ x eps))
0.2b
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
1.8b
(cos (/ (+ x (+ x eps)) 2))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l* sum-log distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative sin-cos-mult cbrt-unprod flip-+ unswap-sqr
Counts
3 → 41
Calls
3 calls:
5.0ms
(+ x (+ x eps))
7.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

series20.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
04826542
14826542

prune106.0ms

Filtered
38 candidates to 50 candidates (-31.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New44650
Fresh022
Picked011
Done000
Total44953

Merged error: 0.2b

Counts
53 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.4b
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
0.5b
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
1.8b
(cos (/ (+ x (+ x eps)) 2))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
24×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×unswap-sqr
4×add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3 associate-*l*
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 85
Calls
4 calls:
8.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
2.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
2.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series34.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
5.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
12.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
5.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify52.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052261255

prune160.0ms

Filtered
56 candidates to 97 candidates (-73.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New94397
Fresh257
Picked101
Done011
Total979106

Merged error: 0.2b

Counts
106 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9))
0.4b
(cbrt (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9)))
1.0b
(pow (cos (/ (+ x (+ x eps)) 2)) 9)
1.8b
(cos (/ (+ x (+ x eps)) 2))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow sqr-pow
2×pow1/3
1×pow-to-exp pow-pow pow-exp
Counts
4 → 57
Calls
4 calls:
2.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9))
2.0ms
(cbrt (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9)))
2.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 9)
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series44.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9))
5.0ms
(cbrt (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9)))
21.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 9)
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify45.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05090972

prune145.0ms

Filtered
53 candidates to 69 candidates (-30.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New69069
Fresh077
Picked011
Done011
Total69978

Merged error: 0.2b

Counts
78 → 9

regimes173.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.6b

bsearch51.0ms

Steps
ItersRangePoint
2
2.0625102901342882e-26
2.28364435969521e-26
2.2560026010000947e-26
7
-0.002551411388017163
-1.3177544881852636e-05
-1.3403420124440877e-05

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03538
13538

end0.0ms

analyze1.0ms

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

sample3.1s

Algorithm
intervals
Results
1.6s3274×body1280valid
607.0ms618×body2560valid
528.0ms1824×body640valid
152.0ms774×body320valid
70.0ms1143×body80valid
47.0ms367×body160valid

Profiling

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