Details

Time bar (total: 4.4s)

analyze2.0ms

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

sample99.0ms

Algorithm
intervals
Results
52.0ms115×body1280valid
21.0ms60×body640valid
9.0ms10×body2560valid
4.0ms25×body320valid
2.0ms33×body80valid
2.0ms13×body160valid

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: 34.7b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (sin (+ x eps)) (sin x))
3.8b
(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))
4.0ms
(sin (+ x eps))

simplify43.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05348268

prune46.0ms

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: 0.6b

Counts
30 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (+ x eps))
0.3b
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.6b
(cos (/ (+ x (+ x eps)) 2))

rewrite18.0ms

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 2)) (cos (/ (+ x (+ x eps)) 2)))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series22.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (+ x eps))
12.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify54.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
05169541

prune124.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New41950
Fresh022
Picked011
Done000
Total411253

Merged error: 0.6b

Counts
53 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (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)
3.6b
(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))

series37.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
7.0ms
(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
13.0ms
(pow (cos (/ (+ x (+ x eps)) 2)) 3)
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify39.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
049241255
149241255

prune166.0ms

Filtered
53 candidates to 97 candidates (-83.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh1910
Picked101
Done011
Total9811109

Merged error: 0.6b

Counts
109 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cos (/ (+ x (+ x eps)) 2)))
3.6b
(cos (/ (+ x (+ x eps)) 2))
3.6b
(cos (/ (+ x (+ x eps)) 2))
3.6b
(cos (/ (+ x (+ x eps)) 2))

rewrite23.0ms

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
1×pow1/3
Counts
4 → 32
Calls
4 calls:
1.0ms
(cbrt (cos (/ (+ x (+ x eps)) 2)))
7.0ms
(cos (/ (+ x (+ x eps)) 2))
7.0ms
(cos (/ (+ x (+ x eps)) 2))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series33.0ms

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

simplify68.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
04872415
14872415

prune119.0ms

Filtered
37 candidates to 44 candidates (-18.9%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New44044
Fresh099
Picked011
Done011
Total441155

Merged error: 0.6b

Counts
55 → 11

regimes201.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.6b

bsearch72.0ms

Steps
ItersRangePoint
9
3.462498710474469e-27
5.680949792135412e-21
5.612773139279313e-21
7
-8.62656504316738e-09
-4.556839319155306e-10
-6.754882924857558e-09

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04751
14751

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s3319×body1280valid
616.0ms644×body2560valid
489.0ms1752×body640valid
163.0ms792×body320valid
68.0ms1083×body80valid
52.0ms410×body160valid

Profiling

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