Details

sample209.0ms

Algorithm

intervals

Results

56.0ms	264×	body	80	valid
51.0ms	26×	body	320	valid
35.0ms	39×	body	640	valid
35.0ms	25×	body	1280	valid
6.0ms	15×	body	160	valid

simplify711.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
40.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite232.0ms

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:

88.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
13.0ms	(cos (/ (+ phi1 phi2) 2))
13.0ms	(cos (/ (+ phi1 phi2) 2))
114.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series744.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
38.0ms	(cos (/ (+ phi1 phi2) 2))
38.0ms	(cos (/ (+ phi1 phi2) 2))
524.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.9s

Counts

151 → 151

Iterations

Iter	Nodes
2	6665
1	1344
0	460

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.7b

localize55.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
40.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite450.0ms

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))
11.0ms	(cos (/ (+ phi1 phi2) 2))
421.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2))
28.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
575.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.8s

Counts

116 → 116

Iterations

Iter	Nodes
2	6979
1	1262
0	425

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.9b

localize82.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
4.2b	(cos (/ (+ phi1 phi2) 2))
40.2b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite571.0ms

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))
7.0ms	(cos (/ (+ phi1 phi2) 2))
544.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

series688.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cos (/ (+ phi1 phi2) 2))
31.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
597.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.1s

Counts

116 → 116

Iterations

Iter	Nodes
2	7019
1	1270
0	427

prune2.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 28.9b

localize81.0ms

Local error

Found 4 expressions with local error:

31.4b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
31.4b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
31.4b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
40.2b	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

29930×	`associate-*l/`
20428×	`frac-times`
16050×	`flip3--` `flip--`
15576×	`cbrt-div`
5990×	`associate-*r/`
5826×	`sqrt-div`
5824×	`frac-add`
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×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5894

Calls

4 calls:

54.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
65.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
110.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
371.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
323.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
344.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
578.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.4m

Counts

5906 → 5906

Iterations

Iter	Nodes
1	57410
0	22401

prune3.2m

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 28.9b

regimes656.0ms

Accuracy

38.8% (8.1b remaining)

Error of 32.2b against oracle of 24.1b and baseline of 37.4b

bsearch165.0ms

Steps

Iters	Range		Point
9	1.3466445914613635e+102	3.62404897155225e+110	7.191645331488462e+104

simplify8.0ms

Iterations

Iter	Nodes
2	37
1	37
0	28

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	8378×	body	80	valid
974.0ms	1309×	body	640	valid
806.0ms	784×	body	1280	valid
628.0ms	730×	body	320	valid
107.0ms	356×	body	160	valid