Details

Time bar (total: 8.5s)

sample205.0ms

Algorithm
intervals
Results
93.0ms112×body1280valid
43.0ms61×body640valid
34.0ms19×body2560valid
7.0ms22×body320valid
4.0ms34×body80valid
2.0ms8×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0717
1717

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.5b

Counts
2 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (sin (+ x eps)) (sin x))
4.6b
(sin (+ x eps))

rewrite22.0ms

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 → 24
Calls
2 calls:
12.0ms
(- (sin (+ x eps)) (sin x))
8.0ms
(sin (+ x eps))

series25.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(- (sin (+ x eps)) (sin x))
9.0ms
(sin (+ x eps))

simplify79.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
05348271

prune98.0ms

Filtered
23 candidates to 30 candidates (-30.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New26430
Fresh000
Picked101
Done000
Total27431

Merged error: 0.3b

Counts
31 → 4

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (+ x eps))
0.2b
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
4.7b
(cos (/ (+ x (+ x eps)) 2))

rewrite40.0ms

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:
14.0ms
(+ x (+ x eps))
11.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
14.0ms
(cos (/ (+ x (+ x eps)) 2))

series39.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ x (+ x eps))
21.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
10.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify99.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
05169541

prune229.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New43750
Fresh123
Picked011
Done000
Total441054

Merged error: 0.3b

Counts
54 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.5b
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
0.6b
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
4.7b
(cos (/ (+ x (+ x eps)) 2))

rewrite44.0ms

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:
16.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
4.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
7.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
14.0ms
(cos (/ (+ x (+ x eps)) 2))

series59.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
10.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
23.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
10.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify64.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049241255
149241255

prune343.0ms

Filtered
55 candidates to 97 candidates (-76.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh178
Picked101
Done011
Total9710107

Merged error: 0.3b

Counts
107 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9)))
0.5b
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9))
1.2b
(pow (cos (/ (+ x (+ x eps)) 2)) 9)
4.7b
(cos (/ (+ x (+ x eps)) 2))

rewrite30.0ms

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:
5.0ms
(cbrt (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9)))
4.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9))
4.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 9)
15.0ms
(cos (/ (+ x (+ x eps)) 2))

series93.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(cbrt (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9)))
25.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 9))
46.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 9)
10.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify67.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05086992

prune333.0ms

Filtered
55 candidates to 69 candidates (-25.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New69069
Fresh088
Picked011
Done011
Total691079

Merged error: 0.3b

Counts
79 → 10

regimes348.0ms

Accuracy

98% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 15.6b

bsearch142.0ms

Steps
ItersRangePoint
8
2.0275204824691034e-25
9.437536156107129e-23
9.346320854214707e-23
9
-1.1294785154268786e-05
-2.51237587459879e-12
-7.340102683950476e-09

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04538
14538

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.2s3342×body1280valid
999.0ms570×body2560valid
919.0ms1823×body640valid
271.0ms753×body320valid
126.0ms1160×body80valid
88.0ms352×body160valid

Profiling

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