Details

Time bar (total: 4.6s)

analyze2.0ms

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

sample106.0ms

Algorithm
intervals
Results
51.0ms143×body1280valid
24.0ms27×body2560valid
12.0ms51×body640valid
9.0ms23×body320valid
1.0ms10×body160valid
0.0ms2×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0777
1777

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.6b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (cos (+ x eps)) (cos x))
3.1b
(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:
6.0ms
(- (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))

simplify54.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
04957270
14957270

prune63.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -2 (* (sin (* eps 1/2)) (sin (* (+ x (+ x eps)) 1/2))))
0.0b
(+ x (+ x eps))
0.3b
(* (sin (* eps 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
3.1b
(sin (* (+ x (+ x eps)) 1/2))

rewrite22.0ms

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:
7.0ms
(* -2 (* (sin (* eps 1/2)) (sin (* (+ x (+ x eps)) 1/2))))
6.0ms
(+ x (+ x eps))
6.0ms
(* (sin (* eps 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
2.0ms
(sin (* (+ x (+ x eps)) 1/2))

series38.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* -2 (* (sin (* eps 1/2)) (sin (* (+ x (+ x eps)) 1/2))))
4.0ms
(+ x (+ x eps))
11.0ms
(* (sin (* eps 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
9.0ms
(sin (* (+ x (+ x eps)) 1/2))

simplify49.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04890766
14890766

prune171.0ms

Filtered
54 candidates to 72 candidates (-33.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New621072
Fresh325
Picked011
Done000
Total651378

Merged error: 0.4b

Counts
78 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin (+ x (* eps 1/2))))
3.1b
(sin (+ x (* eps 1/2)))
3.1b
(sin (+ x (* eps 1/2)))
3.1b
(sin (* (+ x (+ x eps)) 1/2))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod
2×sin-sum
1×pow1/3
Counts
4 → 34
Calls
4 calls:
3.0ms
(cbrt (sin (+ x (* eps 1/2))))
4.0ms
(sin (+ x (* eps 1/2)))
4.0ms
(sin (+ x (* eps 1/2)))
2.0ms
(sin (* (+ x (+ x eps)) 1/2))

series38.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(cbrt (sin (+ x (* eps 1/2))))
7.0ms
(sin (+ x (* eps 1/2)))
5.0ms
(sin (+ x (* eps 1/2)))
6.0ms
(sin (* (+ x (+ x eps)) 1/2))

simplify48.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
04905392
14905392

prune186.0ms

Filtered
38 candidates to 46 candidates (-21.1%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New43346
Fresh2911
Picked101
Done011
Total461359

Merged error: 0.4b

Counts
59 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin (+ x (* eps 1/2))))
0.6b
(cbrt (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
3.1b
(sin (+ x (* eps 1/2)))
3.1b
(sin (* (+ x (+ x eps)) 1/2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
2×cbrt-div pow1/3
1×flip3-+ sin-sum flip-+
Counts
4 → 39
Calls
4 calls:
3.0ms
(cbrt (sin (+ x (* eps 1/2))))
6.0ms
(cbrt (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
4.0ms
(sin (+ x (* eps 1/2)))
2.0ms
(sin (* (+ x (+ x eps)) 1/2))

series65.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(cbrt (sin (+ x (* eps 1/2))))
35.0ms
(cbrt (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
5.0ms
(sin (+ x (* eps 1/2)))
6.0ms
(sin (* (+ x (+ x eps)) 1/2))

simplify64.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
04877689
14877689

prune169.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New47451
Fresh11011
Picked101
Done011
Total491564

Merged error: 0.4b

Counts
64 → 15

regimes259.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch80.0ms

Steps
ItersRangePoint
9
7.875738245108784e-13
4.0456131822497304e-07
4.0014569438137e-07
11
-6001.982300790896
-1.0547417790002664e-17
-0.00010550978972917479

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
015651
115651

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s4497×body1280valid
607.0ms665×body2560valid
418.0ms1798×body640valid
107.0ms674×body320valid
33.0ms293×body160valid
4.0ms73×body80valid

Profiling

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