Details

Time bar (total: 9.5s)

sample59.0ms

Algorithm
intervals
Results
16.0ms257×body80valid
11.0ms37×body640valid
9.0ms22×body1280valid
4.0ms21×body320valid
2.0ms13×body160valid

simplify51.0ms

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: 36.5b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.0b
(cos (/ (+ phi1 phi2) 2.0))
3.0b
(cos (/ (+ phi1 phi2) 2.0))
34.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite57.0ms

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))
9.0ms
(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))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
402.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify61.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013733925
150013756

prune401.0ms

Filtered
147 candidates to 77 candidates (52.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1416147
Fresh000
Picked011
Done000
Total1417148

Merged error: 26.1b

Counts
148 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi1 phi2) 2.0))
3.0b
(cos (/ (+ phi1 phi2) 2.0))
3.0b
(cos (/ (+ phi1 phi2) 2.0))
34.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series674.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
594.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify67.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012784428
150014345

prune520.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1102112
Fresh055
Picked101
Done011
Total1118119

Merged error: 26.1b

Counts
119 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi1 phi2) 2.0))
3.0b
(cos (/ (+ phi1 phi2) 2.0))
3.0b
(cos (/ (+ phi1 phi2) 2.0))
34.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
8.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
400.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify72.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012854577
150014513

prune611.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1120112
Fresh066
Picked011
Done011
Total1128120

Merged error: 26.1b

Counts
120 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

3.0b
(cos (/ (+ phi1 phi2) 2.0))
34.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
34.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
34.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
384×associate-*l/
288×flip3-- flip--
198×sqrt-div
192×frac-times frac-add
96×associate-*r/
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 244
Calls
4 calls:
8.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
27.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
29.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts
4 → 12
Calls
4 calls:
33.0ms
(cos (/ (+ phi1 phi2) 2.0))
407.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
406.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
408.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify143.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0127812868
1500112675

prune1.7s

Filtered
256 candidates to 177 candidates (69.1%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2551256
Fresh055
Picked011
Done022
Total2559264

Merged error: 26.1b

Counts
264 → 9

regimes641.0ms

Accuracy

74.4% (3.5b remaining)

Error of 29.0b against oracle of 25.5b and baseline of 39.3b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03353
13353

end0.0ms

sample1.8s

Algorithm
intervals
Results
542.0ms8406×body80valid
382.0ms1357×body640valid
302.0ms750×body1280valid
151.0ms709×body320valid
54.0ms367×body160valid

Profiling

Loading profile data...