Details

sample212.0ms

Algorithm

intervals

Results

53.0ms	289×	body	80	valid
52.0ms	30×	body	1280	valid
41.0ms	49×	body	640	valid
10.0ms	17×	body	320	valid
5.0ms	14×	body	160	valid

simplify6.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
5	2141
4	757
3	225
2	66
1	32
0	17

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize187.0ms

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))
33.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite957.0ms

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:

218.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
34.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
651.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

282.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
61.0ms	(cos (/ (+ phi1 phi2) 2.0))
42.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.2s	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5002
1	1360
0	461

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.6b

localize250.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.0b	(cos (/ (+ phi1 phi2) 2.0))
3.0b	(cos (/ (+ phi1 phi2) 2.0))
33.5b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite891.0ms

Algorithm

rewrite-expression-head

Rules

146×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

81.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
43.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
701.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
69.0ms	(cos (/ (+ phi1 phi2) 2.0))
66.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.4s	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.5s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
1	1305
0	457

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.5b

localize218.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.0b	(cos (/ (+ phi1 phi2) 2.0))
3.0b	(cos (/ (+ phi1 phi2) 2.0))
33.5b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite879.0ms

Algorithm

rewrite-expression-head

Rules

144×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `add-log-exp`
3×	`log-prod` `exp-prod` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+`

Counts

4 → 112

Calls

4 calls:

71.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(cos (/ (+ phi1 phi2) 2.0))
695.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

51.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
59.0ms	(cos (/ (+ phi1 phi2) 2.0))
44.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.3s	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.6s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
1	1281
0	453

prune1.9s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 19.9b

localize291.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
3.0b	(cos (/ (+ phi1 phi2) 2.0))
3.0b	(cos (/ (+ phi1 phi2) 2.0))
33.5b	(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite6.8s

Algorithm

rewrite-expression-head

Rules

1778×	`associate-*l/`
1412×	`frac-times`
1350×	`flip3--` `flip--`
1308×	`cbrt-div`
642×	`sqrt-div`
640×	`frac-add`
370×	`associate-*r/`
30×	`add-sqr-sqrt`
28×	`cbrt-prod`
27×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`pow1`
10×	`swap-sqr`
8×	`associate-r` `associate-l`
6×	`pow1/3` `add-exp-log` `distribute-lft-out--`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-prod`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 729

Calls

4 calls:

112.0ms	(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
38.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(cos (/ (+ phi1 phi2) 2.0))
6.1s	(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

series1.8s

Counts

4 → 12

Calls

4 calls:

353.0ms	(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
66.0ms	(cos (/ (+ phi1 phi2) 2.0))
70.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.3s	(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

simplify10.1s

Counts

741 → 741

Iterations

Iter	Nodes
done	5001
0	3065

prune20.0s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 19.9b

regimes3.9s

Accuracy

9.7% (13.5b remaining)

Error of 37.7b against oracle of 24.1b and baseline of 39.1b

bsearch1.4s

Steps

Iters	Range		Point
10	6.536504502995308e+110	2.1008190481698437e+126	1.1659851827648714e+126
7	-4.241431024674716e-87	-4.050814288799716e-89	-1.7692204660992532e-87
6	-2.3099727800262368e-23	-4.1023748419932704e-24	-4.16714048268465e-24
11	-6.62677359736212e+175	-1.6517060916622868e+149	-1.342595736819271e+154
9	-4.285673599253076e+181	-6.62677359736212e+175	-3.198787512097014e+178
10	-1.3905735574207628e+227	-1.1235209607012039e+217	-2.4779403317554257e+223

simplify174.0ms

Iterations

Iter	Nodes
done	123
5	123
4	122
3	114
2	95
1	77
0	54

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.1s	8371×	body	80	valid
1.3s	773×	body	1280	valid
1.0s	1368×	body	640	valid
478.0ms	731×	body	320	valid
189.0ms	387×	body	160	valid