Details

sample193.0ms

Algorithm

intervals

Results

60.0ms	253×	body	80	valid
37.0ms	28×	body	1280	valid
35.0ms	33×	body	640	valid
28.0ms	30×	body	320	valid
6.0ms	13×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	2001
4	757
3	225
2	66
1	32
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
3.7b	(cos (/ (+ phi1 phi2) 2))
3.7b	(cos (/ (+ phi1 phi2) 2))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite263.0ms

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:

103.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
13.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
126.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
32.0ms	(cos (/ (+ phi1 phi2) 2))
32.0ms	(cos (/ (+ phi1 phi2) 2))
613.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.5s

Counts

151 → 151

Iterations

Iter	Nodes
done	2004
2	2004
1	1357
0	460

prune904.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.2b

localize79.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2))
3.7b	(cos (/ (+ phi1 phi2) 2))
3.7b	(cos (/ (+ phi1 phi2) 2))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

290×	`associate-*l/`
198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
74×	`associate-*r/`
72×	`cbrt-div` `cos-mult`
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 → 176

Calls

4 calls:

12.0ms	(cos (/ (+ phi1 phi2) 2))
10.0ms	(cos (/ (+ phi1 phi2) 2))
10.0ms	(cos (/ (+ phi1 phi2) 2))
179.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
33.0ms	(cos (/ (+ phi1 phi2) 2))
529.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.7s

Counts

188 → 188

Iterations

Iter	Nodes
done	2000
1	2000
0	831

prune3.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.8b

localize145.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
38.3b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

870×	`associate-*l/`
594×	`flip3--` `flip--`
588×	`frac-times`
414×	`sqrt-div`
408×	`frac-add`
222×	`associate-*r/`
216×	`cbrt-div` `cos-mult`
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 → 464

Calls

4 calls:

8.0ms	(cos (/ (+ phi1 phi2) 2))
138.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
527.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
199.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

35.0ms	(cos (/ (+ phi1 phi2) 2))
572.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
546.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
532.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.0s

Counts

476 → 476

Iterations

Iter	Nodes
done	2000
1	2000
0	831

prune11.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.8b

localize81.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ phi1 phi2) 2))
3.7b	(cos (/ (+ phi1 phi2) 2))
9.8b	(/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2))
38.3b	(sqrt (+ (/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-l/` `associate-r/`
33×	`add-cbrt-cube` `add-exp-log`
32×	`frac-times`
26×	`associate-/l/`
24×	`flip3--` `flip--`
15×	`prod-exp` `cbrt-unprod`
11×	`*-un-lft-identity` `flip3-+` `flip-+`
10×	`sqrt-div`
8×	`add-sqr-sqrt` `frac-add`
7×	`cbrt-undiv` `div-exp` `add-cube-cbrt`
5×	`pow1`
4×	`associate-/r*` `times-frac` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`associate-/r/` `distribute-lft-out`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l*`

Counts

4 → 102

Calls

4 calls:

15.0ms	(cos (/ (+ phi1 phi2) 2))
16.0ms	(cos (/ (+ phi1 phi2) 2))
210.0ms	(/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2))
311.0ms	(sqrt (+ (/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

32.0ms	(cos (/ (+ phi1 phi2) 2))
33.0ms	(cos (/ (+ phi1 phi2) 2))
216.0ms	(/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2))
981.0ms	(sqrt (+ (/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	2010
2	2010
1	951
0	287

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 16.3b

regimes1.5s

Accuracy

35.9% (11.8b remaining)

Error of 31.0b against oracle of 19.2b and baseline of 37.6b

bsearch483.0ms

Steps

Iters	Range		Point
6	4.104173140305455e+73	3.475188210167994e+74	1.9145520666455147e+74
11	-2.0352539667786447e+155	-3.839147915743509e+129	-1.3363728798813314e+154

simplify46.0ms

Iterations

Iter	Nodes
done	94
5	94
4	84
3	80
2	70
1	59
0	42

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.1s	8470×	body	80	valid
1.5s	751×	body	1280	valid
1.4s	1272×	body	640	valid
565.0ms	710×	body	320	valid
175.0ms	332×	body	160	valid