Details

Time bar (total: 8.6s)

sample116.0ms

Algorithm
intervals
Results
34.0ms295×body80valid
19.0ms29×body1280valid
17.0ms36×body640valid
10.0ms28×body320valid
4.0ms18×body160valid

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0500232

prune16.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.0b

Counts
2 → 2

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))))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
35.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite61.0ms

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:
17.0ms
(* (* (- 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))
20.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series200.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* (- 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))
153.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify44.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
051216839

prune287.0ms

Filtered
78 candidates to 147 candidates (-88.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1407147
Fresh101
Picked011
Done000
Total1418149

Merged error: 24.5b

Counts
149 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
35.5b
(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))))

rewrite60.0ms

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:
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
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))))

series168.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
152.0ms
(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))))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
055236501

prune372.0ms

Filtered
80 candidates to 112 candidates (-40.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1120112
Fresh066
Picked011
Done011
Total1128120

Merged error: 24.5b

Counts
120 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
35.5b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
35.5b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
35.5b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
288×flip3-- flip--
240×associate-*r/ associate-*l/
198×sqrt-div
192×frac-times frac-add
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:
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
21.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
21.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
154.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
152.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
163.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify119.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0496917951
1496917951

prune1.0s

Filtered
129 candidates to 256 candidates (-98.4%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2560256
Fresh055
Picked011
Done022
Total2568264

Merged error: 24.5b

Counts
264 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(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))))))
35.5b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
192×flip3-- flip--
160×associate-*r/ associate-*l/
132×sqrt-div
128×frac-times frac-add
66×log-div exp-diff
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:
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
30.0ms
(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))))
20.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
151.0ms
(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))))
156.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify84.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0496412285
1496412285

prune362.0ms

Filtered
99 candidates to 191 candidates (-92.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1865191
Fresh134
Picked101
Done033
Total18811199

Merged error: 24.2b

Counts
199 → 11

regimes1.3s

Accuracy

68.7% (4.5b remaining)

Error of 29.7b against oracle of 25.2b and baseline of 39.5b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033108
133108

end0.0ms

sample3.3s

Algorithm
intervals
Results
901.0ms8404×body80valid
629.0ms1298×body640valid
606.0ms883×body1280valid
280.0ms798×body320valid
91.0ms382×body160valid

Profiling

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