Details

Time bar (total: 4.6s)

analyze2.0ms

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

sample112.0ms

Algorithm
intervals
Results
50.0ms112×body1280valid
26.0ms27×body2560valid
13.0ms44×body640valid
7.0ms15×body160valid
5.0ms27×body320valid
2.0ms31×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0777
1777

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.0b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (sin (+ x eps)) (sin x))
3.2b
(sin (+ 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 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))

simplify42.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
04969268
14969268

prune53.0ms

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: 0.4b

Counts
30 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (+ x eps))
0.3b
(* (sin (* eps 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
3.2b
(cos (* (+ x (+ x eps)) 1/2))

rewrite14.0ms

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))
5.0ms
(* (sin (* eps 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
2.0ms
(cos (* (+ x (+ x eps)) 1/2))

series20.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (+ x eps))
10.0ms
(* (sin (* eps 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
6.0ms
(cos (* (+ x (+ x eps)) 1/2))

simplify48.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
04914470
14914470

prune122.0ms

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

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New45550
Fresh022
Picked011
Done000
Total45853

Merged error: 0.3b

Counts
53 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin (* eps 1/2)))
0.6b
(cbrt (sin (* eps 1/2)))
0.6b
(cbrt (sin (* eps 1/2)))
3.2b
(cos (+ x (* eps 1/2)))

rewrite9.0ms

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
1×cos-sum
Counts
4 → 41
Calls
4 calls:
2.0ms
(cbrt (sin (* eps 1/2)))
2.0ms
(cbrt (sin (* eps 1/2)))
2.0ms
(cbrt (sin (* eps 1/2)))
4.0ms
(cos (+ x (* eps 1/2)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cbrt (sin (* eps 1/2)))
18.0ms
(cbrt (sin (* eps 1/2)))
18.0ms
(cbrt (sin (* eps 1/2)))
5.0ms
(cos (+ x (* eps 1/2)))

simplify56.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
04954414
14954414

prune195.0ms

Filtered
42 candidates to 53 candidates (-26.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New50353
Fresh246
Picked101
Done011
Total53861

Merged error: 0.1b

Counts
61 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (sin (* eps 1/2))) (cbrt (sin (* eps 1/2))))
0.6b
(cbrt (sin (* eps 1/2)))
0.6b
(cbrt (sin (* eps 1/2)))
0.6b
(cbrt (sin (* eps 1/2)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt (sin (* eps 1/2))) (cbrt (sin (* eps 1/2))))
2.0ms
(cbrt (sin (* eps 1/2)))
2.0ms
(cbrt (sin (* eps 1/2)))
2.0ms
(cbrt (sin (* eps 1/2)))

series79.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (cbrt (sin (* eps 1/2))) (cbrt (sin (* eps 1/2))))
18.0ms
(cbrt (sin (* eps 1/2)))
20.0ms
(cbrt (sin (* eps 1/2)))
18.0ms
(cbrt (sin (* eps 1/2)))

simplify51.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
05026705

prune254.0ms

Filtered
61 candidates to 85 candidates (-39.3%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New79685
Fresh156
Picked011
Done011
Total801393

Merged error: 0.0b

Counts
93 → 13

regimes206.0ms

Accuracy

0% (1.3b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09635
19635

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s3317×body1280valid
639.0ms665×body2560valid
496.0ms1776×body640valid
150.0ms757×body320valid
74.0ms1127×body80valid
49.0ms358×body160valid

Profiling

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