Details

Time bar (total: 13.9s)

sample173.0ms

Algorithm
intervals
Results
93.0ms87×body1280valid
36.0ms58×body640valid
13.0ms82×body80valid
9.0ms21×body320valid
2.0ms8×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune5.0ms

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: 0.4b

Counts
2 → 1

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
3.8b
(- (cos x) (cos y))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
31×associate-*l*
22×*-un-lft-identity
18×associate-*r*
12×add-cube-cbrt
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/ sqrt-prod
9×flip3-- flip-- difference-of-squares unswap-sqr
8×add-log-exp
6×sub-neg
5×distribute-lft-out--
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down prod-exp cbrt-unprod
3×times-frac *-commutative
2×diff-log associate-*l/
1×diff-cos
Counts
4 → 115
Calls
4 calls:
22.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series294.0ms

Counts
4 → 10
Calls
4 calls:
141.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
59.0ms
(- (cos x) (cos y))

simplify70.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
06481374
127411282
250031282

prune608.0ms

Filtered
125 candidates to 85 candidates (68.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1178125
Fresh000
Picked101
Done000
Total1188126

Merged error: 0.3b

Counts
126 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
3.8b
(- (cos x) (cos y))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
245×associate-*l*
187×add-sqr-sqrt
156×distribute-lft-out
128×times-frac
107×associate-*r*
66×sqrt-prod unswap-sqr
61×add-cube-cbrt
44×associate-*r/
30×associate-*l/ associate-/r/
28×frac-add
24×associate-/r*
19×associate-/l*
18×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
13×pow1
11×*-commutative difference-of-squares
10×flip3-- flip--
8×add-log-exp
7×prod-exp cbrt-unprod
6×pow-prod-down associate-/l/ distribute-lft-out--
4×frac-times sub-neg
3×frac-2neg clear-num
2×cbrt-undiv distribute-rgt-in distribute-lft-in diff-log div-exp
1×div-inv diff-cos
Counts
4 → 324
Calls
4 calls:
110.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
43.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series1.6s

Counts
4 → 10
Calls
4 calls:
1.4s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
150.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
56.0ms
(- (cos x) (cos y))

simplify127.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0174711715
1500211005

prune1.2s

Filtered
334 candidates to 163 candidates (48.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New32410334
Fresh617
Picked101
Done000
Total33111342

Merged error: 0.0b

Counts
342 → 11

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))) (/ (+ (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))) 2.0) 3.0))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
3.8b
(- (cos x) (cos y))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
536×*-un-lft-identity
269×distribute-lft-out
241×associate-*l*
225×frac-times
198×associate-/r*
176×associate-/l*
158×add-sqr-sqrt
99×add-cube-cbrt
56×times-frac
43×associate-*l/
36×associate-/l/
35×clear-num
34×frac-2neg
31×flip3-+ associate-*r* flip-+
30×associate-/r/
28×add-exp-log frac-add
18×add-cbrt-cube
17×associate-*r/
9×prod-exp difference-of-squares
8×pow1 div-exp add-log-exp unswap-sqr
7×sqrt-prod
5×flip3-- un-div-inv flip-- cbrt-unprod distribute-lft-out--
4×cbrt-undiv sub-neg
2×distribute-rgt-in rec-exp distribute-lft-in diff-log 1-exp pow-prod-down *-commutative div-inv
1×diff-cos
Counts
4 → 434
Calls
4 calls:
126.0ms
(* (/ 1 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))) (/ (+ (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))) 2.0) 3.0))
11.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
5.0ms
(- (cos x) (cos y))

series1.7s

Counts
4 → 10
Calls
4 calls:
1.4s
(* (/ 1 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))) (/ (+ (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))) 2.0) 3.0))
284.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
73.0ms
(- (cos x) (cos y))

simplify158.0ms

Algorithm
egg-herbie
Counts
444 → 444
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0184714913
1500214512

prune1.3s

Filtered
444 candidates to 177 candidates (39.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4404444
Fresh4610
Picked101
Done000
Total44510455

Merged error: 0.0b

Counts
455 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(- 3.0 (sqrt 5.0))
3.8b
(- (cos x) (cos y))
3.8b
(- (cos x) (cos y))
3.8b
(- (cos x) (cos y))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-log-exp
5×difference-of-squares
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out--
3×diff-cos
1×sqrt-prod
Counts
4 → 60
Calls
4 calls:
7.0ms
(- 3.0 (sqrt 5.0))
5.0ms
(- (cos x) (cos y))
4.0ms
(- (cos x) (cos y))
4.0ms
(- (cos x) (cos y))

series178.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(- 3.0 (sqrt 5.0))
61.0ms
(- (cos x) (cos y))
61.0ms
(- (cos x) (cos y))
55.0ms
(- (cos x) (cos y))

simplify66.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0219421
1587395
22253389
35002389

prune415.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New69170
Fresh189
Picked011
Done000
Total701080

Merged error: 0.0b

Counts
80 → 10

regimes195.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06474
17474
28474
38474

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.9s2720×body1280valid
1.2s1788×body640valid
356.0ms772×body320valid
339.0ms2398×body80valid
110.0ms322×body160valid