Details

sample142.0ms

Algorithm

intervals

Results

50.0ms	259×	body	80	valid
19.0ms	39×	body	640	valid
17.0ms	25×	body	1280	valid
7.0ms	17×	body	320	valid
2.0ms	9×	body	160	valid

simplify6.2s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite402.0ms

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:

129.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cos (/ (+ phi1 phi2) 2.0))
196.0ms	(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:

283.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
54.0ms	(cos (/ (+ phi1 phi2) 2.0))
67.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.3s	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.1s

Counts

151 → 151

Iterations

Iter	Nodes
done	5002
1	1360
0	461

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.4b

localize137.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite420.0ms

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:

17.0ms	(cos (/ (+ phi1 phi2) 2.0))
32.0ms	(cos (/ (+ phi1 phi2) 2.0))
33.0ms	(cos (/ (+ phi1 phi2) 2.0))
275.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

66.0ms	(cos (/ (+ phi1 phi2) 2.0))
68.0ms	(cos (/ (+ phi1 phi2) 2.0))
64.0ms	(cos (/ (+ phi1 phi2) 2.0))
1.2s	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify5.5s

Counts

188 → 188

Iterations

Iter	Nodes
done	5002
1	2496
0	832

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.8b

localize124.0ms

Local error

Found 4 expressions with local error:

3.3b	(cos (/ (+ phi1 phi2) 2.0))
3.3b	(cos (/ (+ phi1 phi2) 2.0))
25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
34.9b	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.4s

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:

16.0ms	(cos (/ (+ phi1 phi2) 2.0))
16.0ms	(cos (/ (+ phi1 phi2) 2.0))
198.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
1.2s	(sqrt (+ (exp (log (* (* (- 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:

46.0ms	(cos (/ (+ phi1 phi2) 2.0))
64.0ms	(cos (/ (+ phi1 phi2) 2.0))
415.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
1.2s	(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.9s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
1	1208
0	473

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.5b

localize317.0ms

Local error

Found 4 expressions with local error:

25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
25.8b	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
34.9b	(sqrt (+ (exp (* (* (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite510.0ms

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:

137.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
177.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
167.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
14.0ms	(sqrt (+ (exp (* (* (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))) (* (- phi1 phi2) (- phi1 phi2))))

series2.4s

Counts

4 → 12

Calls

4 calls:

387.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
347.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
406.0ms	(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
1.2s	(sqrt (+ (exp (* (* (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))))) (cbrt (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify6.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5006
3	4549
2	1024
1	354
0	130

prune1.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.5b

regimes3.0s

Accuracy

33.1% (11.1b remaining)

Error of 33.7b against oracle of 22.6b and baseline of 39.2b

bsearch128.0ms

Steps

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

simplify23.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.7s	1299×	body	640	valid
1.4s	8247×	body	80	valid
755.0ms	841×	body	1280	valid
359.0ms	735×	body	320	valid
122.0ms	374×	body	160	valid