Details

sample165.0ms

Algorithm

intervals

Results

63.0ms	259×	body	80	valid
29.0ms	39×	body	640	valid
26.0ms	25×	body	1280	valid
11.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2141
4	757
3	225
2	66
1	32
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
3.3b	(cos (/ (+ phi1 phi2) 2))
3.3b	(cos (/ (+ phi1 phi2) 2))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite314.0ms

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:

121.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
15.0ms	(cos (/ (+ phi1 phi2) 2))
10.0ms	(cos (/ (+ phi1 phi2) 2))
157.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
34.0ms	(cos (/ (+ phi1 phi2) 2))
36.0ms	(cos (/ (+ phi1 phi2) 2))
506.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.8s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
1	1357
0	460

prune677.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.0b

localize70.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ phi1 phi2) 2))
3.3b	(cos (/ (+ phi1 phi2) 2))
3.3b	(cos (/ (+ phi1 phi2) 2))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

266×	`associate-*l/`
198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`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:

11.0ms	(cos (/ (+ phi1 phi2) 2))
14.0ms	(cos (/ (+ phi1 phi2) 2))
19.0ms	(cos (/ (+ phi1 phi2) 2))
184.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cos (/ (+ phi1 phi2) 2))
22.0ms	(cos (/ (+ phi1 phi2) 2))
37.0ms	(cos (/ (+ phi1 phi2) 2))
643.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.5s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
1	2341
0	789

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.4b

localize84.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ phi1 phi2) 2))
3.3b	(cos (/ (+ phi1 phi2) 2))
25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
34.9b	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite952.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
72×	`log-div`
68×	`frac-times`
66×	`sqrt-div`
64×	`exp-diff` `frac-add`
45×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down` `add-exp-log`
16×	`log-pow`
8×	`prod-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `rem-log-exp` `add-cube-cbrt`
4×	`add-cbrt-cube` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `log-prod` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 134

Calls

4 calls:

11.0ms	(cos (/ (+ phi1 phi2) 2))
10.0ms	(cos (/ (+ phi1 phi2) 2))
99.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
813.0ms	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (/ (+ phi1 phi2) 2))
38.0ms	(cos (/ (+ phi1 phi2) 2))
205.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
604.0ms	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.9s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
1	1215
0	472

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.4b

localize115.0ms

Local error

Found 4 expressions with local error:

25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
34.9b	(sqrt (+ (exp (* (* (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

125×	`pow1`
51×	`pow-prod-down`
48×	`log-pow`
43×	`add-exp-log`
42×	`associate-*l/`
24×	`log-div` `prod-exp`
18×	`flip3--` `flip--`
15×	`rem-log-exp`
12×	`frac-times` `pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `pow-plus` `associate-*r/`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow2` `log-prod` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 130

Calls

4 calls:

121.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
84.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
108.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
30.0ms	(sqrt (+ (exp (* (* (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

158.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
174.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
210.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
532.0ms	(sqrt (+ (exp (* (* (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.9s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
3	4936
2	1047
1	352
0	129

prune929.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.4b

regimes946.0ms

Accuracy

34.4% (9.7b remaining)

Error of 32.2b against oracle of 22.5b and baseline of 37.3b

bsearch114.0ms

Steps

Iters	Range		Point
7	2.3783549764193696e+124	1.0211978030125453e+126	2.511829003669043e+124

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.2s	8247×	body	80	valid
1.1s	841×	body	1280	valid
844.0ms	1299×	body	640	valid
459.0ms	735×	body	320	valid
100.0ms	374×	body	160	valid