Details

sample99.0ms

Algorithm

intervals

Results

19.0ms	44×	body	1280	valid
17.0ms	280×	body	80	nan
11.0ms	196×	body	80	valid
8.0ms	32×	body	640	valid
4.0ms	6×	body	2560	valid
3.0ms	17×	body	320	valid
0.0ms	4×	body	160	valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	33	19
2	58	19
3	82	19
4	97	19
5	104	19
6	106	19
done	106	19

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(/ (* z t) 3.0)
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
24.1b	(cos (- y (/ (* z t) 3.0)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`prod-diff`
19×	`add-exp-log` `add-cbrt-cube`
15×	`times-frac`
9×	`pow1`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 101

Calls

4 calls:

7.0ms	(/ a (* b 3.0))
9.0ms	(/ (* z t) 3.0)
33.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
22.0ms	(cos (- y (/ (* z t) 3.0)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ a (* b 3.0))
21.0ms	(/ (* z t) 3.0)
107.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
44.0ms	(cos (- y (/ (* z t) 3.0)))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	327	2847
1	666	2377
2	1867	1875
done	5000	1638

prune433.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0)))))
0.2b	(* t (/ z (* (cbrt 3.0) (cbrt 3.0))))
0.3b	(/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0))
24.4b	(cos (- y (/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`add-exp-log` `cos-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
30×	`prod-diff`
28×	`times-frac`
24×	`add-cbrt-cube`
15×	`cbrt-prod`
11×	`pow1` `prod-exp` `cbrt-unprod`
10×	`associate-r`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/l/` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

34.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0)))))
28.0ms	(* t (/ z (* (cbrt 3.0) (cbrt 3.0))))
24.0ms	(/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0))
32.0ms	(cos (- y (/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0)))))
136.0ms	(* t (/ z (* (cbrt 3.0) (cbrt 3.0))))
96.0ms	(/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0))
108.0ms	(cos (- y (/ (* t (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt 3.0))))

simplify1.2s

Counts

140 → 140

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	404	6184
1	830	4444
2	2242	3089
done	5000	2570

prune569.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 13.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
0.6b	(cbrt (/ z (pow (cbrt 3.0) 2)))
0.6b	(cbrt (/ z (pow (cbrt 3.0) 2)))
24.2b	(cos (- y (/ (* (* (* (cbrt (/ z (pow (cbrt 3.0) 2))) (cbrt (/ z (pow (cbrt 3.0) 2)))) t) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (cbrt 3.0))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

108×	`cbrt-prod`
87×	`times-frac`
67×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
32×	`cos-sum`
30×	`prod-diff`
6×	`div-inv` `unpow2` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`cos-diff` `sub-neg`

Counts

4 → 156

Calls

4 calls:

6.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
6.0ms	(cbrt (/ z (pow (cbrt 3.0) 2)))
6.0ms	(cbrt (/ z (pow (cbrt 3.0) 2)))
35.0ms	(cos (- y (/ (* (* (* (cbrt (/ z (pow (cbrt 3.0) 2))) (cbrt (/ z (pow (cbrt 3.0) 2)))) t) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (cbrt 3.0))))

series1.7s

Counts

4 → 12

Calls

4 calls:

514.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
506.0ms	(cbrt (/ z (pow (cbrt 3.0) 2)))
497.0ms	(cbrt (/ z (pow (cbrt 3.0) 2)))
157.0ms	(cos (- y (/ (* (* (* (cbrt (/ z (pow (cbrt 3.0) 2))) (cbrt (/ z (pow (cbrt 3.0) 2)))) t) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (cbrt 3.0))))

simplify2.9s

Counts

168 → 168

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	441	10701
1	731	8486
2	1430	4885
3	4979	3475
done	5000	3475

prune1.1s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 13.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0))
0.3b	(/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0))
26.8b	(sin (/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0)))
27.0b	(cos (/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
16×	`div-exp` `add-cbrt-cube`
12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/r`
8×	`cbrt-undiv` `prod-exp`
4×	`pow1` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `associate-l/` `pow-exp` `clear-num` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 86

Calls

4 calls:

17.0ms	(/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0))
22.0ms	(/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0))
5.0ms	(sin (/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0)))
5.0ms	(cos (/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0))
122.0ms	(/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0))
91.0ms	(sin (/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0)))
81.0ms	(cos (/ (* (/ z (pow (cbrt 3.0) 2)) t) (cbrt 3.0)))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: 3 (895.0ms)

Iter	Nodes	Cost
0	106	1384
1	222	1326
2	713	992
3	3617	794
done	5000	794

prune840.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 13.6b

regimes3.5s

Accuracy

47.3% (2.7b remaining)

Error of 18.6b against oracle of 15.9b and baseline of 21.0b

bsearch3.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	104
1	68	104
2	72	104
3	79	104
4	81	104
done	81	104

end0.0ms

sample3.0s

Algorithm

intervals

Results

589.0ms	1602×	body	1280	valid
574.0ms	9072×	body	80	nan
329.0ms	5549×	body	80	valid
249.0ms	964×	body	640	valid
243.0ms	385×	body	2560	valid
80.0ms	435×	body	320	valid
28.0ms	198×	body	160	valid