Details

sample124.0ms

Algorithm

intervals

Results

37.0ms	40×	body	1280	valid
27.0ms	43×	body	640	valid
19.0ms	139×	body	80	valid
9.0ms	22×	body	320	valid
4.0ms	12×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	12	8
2	15	8
done	15	8

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (sin y)) (* z (cos y)))
0.1b	(* x (sin y))
0.1b	(* z (cos y))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 54

Calls

3 calls:

21.0ms	(+ (* x (sin y)) (* z (cos y)))
19.0ms	(* x (sin y))
24.0ms	(* z (cos y))

series306.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(+ (* x (sin y)) (* z (cos y)))
76.0ms	(* x (sin y))
78.0ms	(* z (cos y))

simplify4.2s

Counts

63 → 63

Iterations

Useful iterations: 2 (184.0ms)

Iter	Nodes	Cost
0	88	498
1	208	453
2	717	420
3	4094	420
done	5000	420

prune498.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos y)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

35.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
3.0ms	(cbrt (cos y))

series893.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
193.0ms	(cbrt (cos y))
187.0ms	(cbrt (cos y))
190.0ms	(cbrt (cos y))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	68	726
1	152	651
2	637	551
done	5001	537

prune739.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (sin y))
0.1b	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
0.2b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
13×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`pow1` `associate-r`
6×	`cbrt-prod` `cbrt-unprod`
5×	`pow-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `pow-unpow`
2×	`pow-prod-down` `*-commutative`
1×	`pow-pow` `unpow1/3` `pow1/3` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

24.0ms	(* x (sin y))
82.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
7.0ms	(pow (cos y) 2)
3.0ms	(cbrt (cos y))

series370.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* x (sin y))
63.0ms	(* (* z (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
31.0ms	(pow (cos y) 2)
193.0ms	(cbrt (cos y))

simplify1.6s

Counts

92 → 92

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	133	813
1	344	717
2	1572	636
done	5001	616

prune785.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (cbrt (cos y))))
0.2b	(pow (cos y) 2)
0.3b	(cbrt (cos y))
0.6b	(expm1 (cbrt (cos y)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow`
1×	`pow-to-exp` `log1p-udef` `expm1-log1p` `pow-pow` `pow1/3` `log1p-expm1` `pow-exp` `unpow2` `expm1-udef` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

0.0ms	(log1p (expm1 (cbrt (cos y))))
6.0ms	(pow (cos y) 2)
2.0ms	(cbrt (cos y))
1.0ms	(expm1 (cbrt (cos y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

436.0ms	(log1p (expm1 (cbrt (cos y))))
34.0ms	(pow (cos y) 2)
196.0ms	(cbrt (cos y))
396.0ms	(expm1 (cbrt (cos y)))

simplify3.2s

Counts

67 → 67

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	89	442
1	213	377
2	698	341
3	3011	331
done	5001	327

prune626.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes475.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	18	17
done	18	17

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.2s	4293×	body	80	valid
1.6s	1547×	body	1280	valid
834.0ms	1231×	body	640	valid
253.0ms	595×	body	320	valid
94.0ms	334×	body	160	valid