Details

Time bar (total: 10.2s)

sample66.0ms

Algorithm
intervals
Results
18.0ms287×body80valid
13.0ms23×body1280valid
11.0ms38×body640valid
3.0ms14×body320valid
2.0ms13×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune3.0ms

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: 39.3b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
36.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
68×frac-times
66×sqrt-div
64×frac-add
44×pow1
34×associate-*r/
17×pow-prod-down
16×add-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow-sqr pow-prod-up add-log-exp
3×sqrt-prod
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 135
Calls
4 calls:
13.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
18.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
420.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013733924
150013756

prune450.0ms

Filtered
147 candidates to 77 candidates (52.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1398147
Fresh000
Picked011
Done000
Total1399148

Merged error: 22.5b

Counts
148 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
36.2b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
198×flip3-- flip--
196×frac-times
138×sqrt-div
136×frac-add
130×associate-*l/
74×associate-*r/
73×cos-mult
12×pow1 add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
4×add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqr-cos sqrt-pow1 flip3-+ pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 192
Calls
4 calls:
4.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
411.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify109.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
024717439
150017337

prune636.0ms

Filtered
204 candidates to 102 candidates (50.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2022204
Fresh257
Picked101
Done011
Total2058213

Merged error: 22.5b

Counts
213 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
0.6b
(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
3.3b
(cos (* 2 (/ (+ phi1 phi2) 2.0)))
36.2b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
356×frac-times
318×flip3-- flip--
210×sqrt-div
208×frac-add
178×associate-*l/
124×associate-*r/
83×flip3-+ flip-+
10×pow1
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity add-log-exp
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* sum-log *-commutative cos-2 unswap-sqr
Counts
4 → 289
Calls
4 calls:
14.0ms
(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
3.0ms
(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
2.0ms
(cos (* 2 (/ (+ phi1 phi2) 2.0)))
27.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.7s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0))))))
39.0ms
(+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))
27.0ms
(cos (* 2 (/ (+ phi1 phi2) 2.0)))
1.6s
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (+ 1/2 (* 1/2 (cos (* 2 (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify200.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (62.0ms)

IterNodesCost
0382315482
1500215368

prune1.1s

Filtered
301 candidates to 155 candidates (51.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2992301
Fresh066
Picked011
Done011
Total29910309

Merged error: 22.5b

Counts
309 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

3.3b
(cos (/ (+ phi1 phi2) 2.0))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
6.0b
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
36.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
66×log-div exp-diff
64×associate-*r/
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×log-prod exp-prod exp-sum sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×log-pow
2×sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-sqrt-square rem-exp-log
Counts
4 → 179
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
19.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series887.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
422.0ms
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
412.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify94.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
015136939
150026823

prune608.0ms

Filtered
191 candidates to 99 candidates (51.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1874191
Fresh167
Picked101
Done022
Total18912201

Merged error: 22.5b

Counts
201 → 12

regimes921.0ms

Accuracy

71.7% (4.0b remaining)

Error of 28.9b against oracle of 24.9b and baseline of 38.9b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03353
13353

end0.0ms

sample1.8s

Algorithm
intervals
Results
554.0ms8447×body80valid
376.0ms1318×body640valid
308.0ms761×body1280valid
145.0ms727×body320valid
50.0ms365×body160valid