Details

sample192.0ms

Algorithm

intervals

Results

42.0ms	15×	body	2560	valid
35.0ms	52×	body	1280	valid
32.0ms	314×	body	80	nan
17.0ms	186×	body	80	valid
11.0ms	27×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify362.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	32	19
2	54	19
3	75	19
4	87	19
5	89	19
done	89	19

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.3b	(/ a (* b 3.0))
27.5b	(cos (- y (/ (* z t) 3.0)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`cos-sum` `frac-2neg` `clear-num` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

15.0ms	(/ (* z t) 3.0)
42.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
10.0ms	(/ a (* b 3.0))
24.0ms	(cos (- y (/ (* z t) 3.0)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* z t) 3.0)
112.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
31.0ms	(/ a (* b 3.0))
48.0ms	(cos (- y (/ (* z t) 3.0)))

simplify3.0s

Counts

84 → 84

Iterations

Useful iterations: 2 (229.0ms)

Iter	Nodes	Cost
0	170	993
1	399	961
2	1327	813
3	4801	813
done	5000	813

prune421.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.2b

localize42.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt (/ (* z t) 3.0))
15.0b	(cbrt (/ (* z t) 3.0))
15.0b	(cbrt (/ (* z t) 3.0))
27.4b	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

6.0ms	(cbrt (/ (* z t) 3.0))
6.0ms	(cbrt (/ (* z t) 3.0))
6.0ms	(cbrt (/ (* z t) 3.0))
15.0ms	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0)))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (/ (* z t) 3.0))
147.0ms	(cbrt (/ (* z t) 3.0))
122.0ms	(cbrt (/ (* z t) 3.0))
129.0ms	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0)))))

simplify2.3s

Counts

70 → 70

Iterations

Useful iterations: 5 (822.0ms)

Iter	Nodes	Cost
0	93	1008
1	162	991
2	279	738
3	565	675
4	1010	651
5	2304	636
done	5001	636

prune491.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 18.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ t (sqrt 3.0)))
15.0b	(cbrt (/ (* z t) 3.0))
15.0b	(cbrt (/ (* z t) 3.0))
27.6b	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 73

Calls

4 calls:

4.0ms	(cbrt (/ t (sqrt 3.0)))
4.0ms	(cbrt (/ (* z t) 3.0))
11.0ms	(cbrt (/ (* z t) 3.0))
9.0ms	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

407.0ms	(cbrt (/ t (sqrt 3.0)))
112.0ms	(cbrt (/ (* z t) 3.0))
103.0ms	(cbrt (/ (* z t) 3.0))
772.0ms	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))))))

simplify1.7s

Counts

85 → 85

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	190	1331
1	331	1286
2	669	1185
3	1959	1165
done	5000	1140

prune825.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 17.7b

localize55.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt (/ (* z t) 3.0))
15.0b	(cbrt (/ (* z t) 3.0))
32.1b	(sin (- (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))))))
32.2b	(cos (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0))))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-div` `pow1/3` `div-inv`
1×	`neg-sub0` `sin-neg` `sin-diff`

Counts

4 → 48

Calls

4 calls:

4.0ms	(cbrt (/ (* z t) 3.0))
4.0ms	(cbrt (/ (* z t) 3.0))
50.0ms	(sin (- (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))))))
53.0ms	(cos (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (/ (* z t) 3.0))
122.0ms	(cbrt (/ (* z t) 3.0))
543.0ms	(sin (- (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))))))
287.0ms	(cos (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (cbrt (/ z (sqrt 3.0))) (cbrt (/ t (sqrt 3.0))))))

simplify1.8s

Counts

60 → 60

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	109	1136
1	215	1118
2	514	942
3	1909	928
done	5000	912

prune773.0ms

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 17.5b

regimes5.8s

Accuracy

57.2% (1.8b remaining)

Error of 17.8b against oracle of 16.0b and baseline of 20.1b

bsearch4.0ms

simplify19.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	98
1	80	98
2	91	98
done	91	98

end0.0ms

sample7.3s

Algorithm

intervals

Results

1.8s	9318×	body	80	nan
1.6s	1603×	body	1280	valid
974.0ms	927×	body	640	valid
946.0ms	5704×	body	80	valid
422.0ms	362×	body	2560	valid
148.0ms	432×	body	320	valid
81.0ms	215×	body	160	valid