Details

sample213.0ms

Algorithm

intervals

Results

67.0ms	272×	body	80	valid
51.0ms	26×	body	1280	valid
48.0ms	46×	body	640	valid
13.0ms	18×	body	320	valid
5.0ms	11×	body	160	valid

simplify742.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2141
4	757
3	225
2	66
1	32
0	17

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite180.0ms

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-cbrt-cube` `add-exp-log`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16` `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 → 139

Calls

4 calls:

67.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
8.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
93.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
24.0ms	(cos (/ (+ phi1 phi2) 2))
29.0ms	(cos (/ (+ phi1 phi2) 2))
538.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
2	6655
1	1344
0	460

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize61.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite356.0ms

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` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 104

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
330.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi1 phi2) 2))
30.0ms	(cos (/ (+ phi1 phi2) 2))
35.0ms	(cos (/ (+ phi1 phi2) 2))
458.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.6s

Counts

116 → 116

Iterations

Iter	Nodes
2	6989
1	1264
0	425

prune2.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 25.9b

localize53.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 176

Calls

4 calls:

10.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
73.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
73.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

31.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
559.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
539.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.5s

Counts

188 → 188

Iterations

Iter	Nodes
2	6299
1	1245
0	421

prune5.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 25.9b

localize125.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (/ (+ phi1 phi2) 2))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
37.7b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite387.0ms

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` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 248

Calls

4 calls:

14.0ms	(cos (/ (+ phi1 phi2) 2))
135.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
100.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
119.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.8s

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (/ (+ phi1 phi2) 2))
587.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
581.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
635.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.4s

Counts

260 → 260

Iterations

Iter	Nodes
2	6299
1	1245
0	421

prune7.7s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 25.9b

regimes1.6s

Accuracy

58.7% (5.8b remaining)

Error of 29.2b against oracle of 23.4b and baseline of 37.4b

bsearch3.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	27
1	27
0	22

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.5s	8309×	body	80	valid
1.4s	1335×	body	640	valid
1.4s	767×	body	1280	valid
545.0ms	747×	body	320	valid
205.0ms	365×	body	160	valid