Details

sample157.0ms

Algorithm

intervals

Results

62.0ms	251×	body	80	valid
35.0ms	51×	body	640	valid
20.0ms	21×	body	1280	valid
9.0ms	18×	body	320	valid
4.0ms	14×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
3.9b	(cos (/ (+ phi1 phi2) 2))
3.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite352.0ms

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:

130.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
21.0ms	(cos (/ (+ phi1 phi2) 2))
20.0ms	(cos (/ (+ phi1 phi2) 2))
171.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series849.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
39.0ms	(cos (/ (+ phi1 phi2) 2))
30.0ms	(cos (/ (+ phi1 phi2) 2))
628.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.1s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
1	1357
0	460

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
3.9b	(cos (/ (+ phi1 phi2) 2))
3.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
130×	`associate-*l/`
74×	`associate-*r/`
73×	`cos-mult`
12×	`add-sqr-sqrt` `pow1`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`insert-posit16` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `rem-sqrt-square` `sqr-cos` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 196

Calls

4 calls:

21.0ms	(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
21.0ms	(cos (/ (+ phi1 phi2) 2))
21.0ms	(cos (/ (+ phi1 phi2) 2))
164.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
39.0ms	(cos (/ (+ phi1 phi2) 2))
31.0ms	(cos (/ (+ phi1 phi2) 2))
564.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify3.1s

Counts

208 → 208

Iterations

Iter	Nodes
done	5001
1	2519
0	813

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 25.5b

localize83.0ms

Local error

Found 4 expressions with local error:

26.9b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
26.9b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
26.9b	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
35.9b	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

29930×	`associate-*l/`
20428×	`frac-times`
16050×	`flip3--` `flip--`
15576×	`cbrt-div`
5990×	`associate-*r/`
5826×	`sqrt-div`
5824×	`frac-add`
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×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5894

Calls

4 calls:

76.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
79.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
93.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
940.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

335.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
333.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
329.0ms	(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
586.0ms	(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.1s

Counts

5906 → 5906

Iterations

Iter	Nodes
done	22401
0	22401

prune1.8m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 25.5b

localize57.0ms

Local error

Found 4 expressions with local error:

3.9b	(cos (/ (+ phi1 phi2) 2))
3.9b	(cos (/ (+ phi1 phi2) 2))
27.7b	(posit16->real (real->posit16 (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (posit16->real (real->posit16 (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `associate-*l/` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
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-+` `remove-posit16`

Counts

4 → 105

Calls

4 calls:

10.0ms	(cos (/ (+ phi1 phi2) 2))
10.0ms	(cos (/ (+ phi1 phi2) 2))
0.0ms	(posit16->real (real->posit16 (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))))
84.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (posit16->real (real->posit16 (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cos (/ (+ phi1 phi2) 2))
21.0ms	(cos (/ (+ phi1 phi2) 2))
37.0ms	(posit16->real (real->posit16 (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))))
402.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (posit16->real (real->posit16 (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
1	1240
0	442

prune714.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.2b

regimes610.0ms

Accuracy

36% (8.5b remaining)

Error of 32.1b against oracle of 23.6b and baseline of 36.9b

bsearch91.0ms

Steps

Iters	Range		Point
8	1.1713275423134012e+63	1.2542877675797518e+66	7.088685391289955e+65

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample3.0s

Algorithm

intervals

Results

897.0ms	8406×	body	80	valid
661.0ms	1235×	body	640	valid
587.0ms	745×	body	1280	valid
507.0ms	658×	body	320	valid
71.0ms	403×	body	160	valid