Details

Time bar (total: 5.5s)

sample89.0ms

Algorithm
intervals
Results
51.0ms144×body1280valid
12.0ms14×body2560valid
11.0ms56×body640valid
4.0ms30×body320valid
1.0ms11×body160valid
0.0ms1×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.8b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (cos (+ x eps)) (cos x))
2.6b
(cos (+ 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 cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
6.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series71.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify111.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune86.0ms

Filtered
30 candidates to 23 candidates (76.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New181230
Fresh000
Picked101
Done000
Total191231

Merged error: 16.9b

Counts
31 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
1.9b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sub-neg cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 70
Calls
4 calls:
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
7.0ms
(* (cos x) (cos eps))
4.0ms
(* (sin x) (sin eps))
9.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series300.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
39.0ms
(* (cos x) (cos eps))
48.0ms
(* (sin x) (sin eps))
129.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify115.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0304632
11061600
24488582
35001582

prune216.0ms

Filtered
82 candidates to 57 candidates (69.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh4711
Picked101
Done000
Total781694

Merged error: 16.8b

Counts
94 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(+ (* (sin x) (sin eps)) (cos x))
0.2b
(* (sin x) (sin eps))
1.9b
(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-log-exp
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
3×cos-mult
2×flip3-+ diff-log pow-prod-down prod-exp sum-log *-commutative frac-sub cbrt-unprod flip-+ unswap-sqr
1×+-commutative sub-neg flip3-- flip-- sin-mult associate--r+
Counts
4 → 65
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(+ (* (sin x) (sin eps)) (cos x))
4.0ms
(* (sin x) (sin eps))
9.0ms
(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos x) (cos eps))
51.0ms
(+ (* (sin x) (sin eps)) (cos x))
48.0ms
(* (sin x) (sin eps))
129.0ms
(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0332607
11284574
25002565

prune226.0ms

Filtered
77 candidates to 53 candidates (68.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New69877
Fresh31215
Picked101
Done000
Total732093

Merged error: 16.7b

Counts
93 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.2b
(* (cos x) (cos x))
0.3b
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
3.1b
(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
52×pow1
20×add-exp-log add-cbrt-cube
19×pow-prod-down
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity prod-exp cbrt-unprod
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-sqr pow-prod-up sin-mult
4×swap-sqr
3×pow-plus *-commutative
2×pow2 cos-mult unswap-sqr
1×frac-times sub-neg sqr-cos flip3-- diff-log div-sub associate-*r/ associate-*l/ frac-sub flip-- associate--r-
Counts
4 → 97
Calls
4 calls:
4.0ms
(* (sin x) (sin eps))
4.0ms
(* (cos x) (cos x))
12.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
14.0ms
(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin x) (sin eps))
17.0ms
(* (cos x) (cos x))
57.0ms
(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
305.0ms
(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

simplify58.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0397966
11716822
25002770

prune224.0ms

Filtered
109 candidates to 60 candidates (55.0%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh31619
Picked101
Done000
Total11019129

Merged error: 16.7b

Counts
129 → 19

regimes200.0ms

Accuracy

84.3% (1.5b remaining)

Error of 15.8b against oracle of 14.3b and baseline of 24.1b

bsearch126.0ms

Steps
ItersRangePoint
10
1.8195789593932265e-08
39972.03059165128
8.124848288377058e-08
8
-0.1213939224205488
-3.1026666635640823e-06
-3.159721763837506e-06

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04444
14444

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s4444×body1280valid
568.0ms670×body2560valid
389.0ms1828×body640valid
93.0ms674×body320valid
30.0ms306×body160valid
4.0ms78×body80valid

Profiling

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