Details

sample165.0ms

Algorithm

intervals

Results

62.0ms	49×	body	640	valid
44.0ms	289×	body	80	valid
25.0ms	30×	body	1280	valid
8.0ms	17×	body	320	valid
5.0ms	14×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4415
4	917
3	240
2	69
1	32
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize39.0ms

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))
33.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite230.0ms

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))))
15.0ms	(cos (/ (+ phi1 phi2) 2))
16.0ms	(cos (/ (+ phi1 phi2) 2))
93.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
23.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
931.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

151 → 151

Iterations

Iter	Nodes
done	5002
1	1387
0	460

prune813.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
33.5b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite286.0ms

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:

19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
15.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
234.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
26.0ms	(cos (/ (+ phi1 phi2) 2))
42.0ms	(cos (/ (+ phi1 phi2) 2))
512.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.7s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
1	1323
0	456

prune934.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2))))
3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
33.5b	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite287.0ms

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:

27.0ms	(log (exp (cos (/ (+ phi1 phi2) 2))))
15.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
223.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(log (exp (cos (/ (+ phi1 phi2) 2))))
25.0ms	(cos (/ (+ phi1 phi2) 2))
29.0ms	(cos (/ (+ phi1 phi2) 2))
587.0ms	(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
1	1298
0	452

prune862.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 19.8b

localize78.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
3.0b	(cos (/ (+ phi1 phi2) 2))
3.0b	(cos (/ (+ phi1 phi2) 2))
33.5b	(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.0s

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:

37.0ms	(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
14.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
1.8s	(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))
35.0ms	(cos (/ (+ phi1 phi2) 2))
36.0ms	(cos (/ (+ phi1 phi2) 2))
595.0ms	(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify6.2s

Counts

741 → 741

Iterations

Iter	Nodes
done	5000
0	3064

prune11.9s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 19.8b

regimes1.6s

Accuracy

37.2% (8.4b remaining)

Error of 32.2b against oracle of 23.8b and baseline of 37.2b

bsearch300.0ms

Steps

Iters	Range		Point
10	-4.8371989502428525e+86	-4.387318315737689e+71	-4.23733770204599e+84

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.2s	8371×	body	80	valid
1.4s	1368×	body	640	valid
1.1s	773×	body	1280	valid
479.0ms	731×	body	320	valid
157.0ms	387×	body	160	valid