Details

sample118.0ms

Algorithm

intervals

Results

45.0ms	50×	body	1280	valid
23.0ms	39×	body	640	valid
18.0ms	138×	body	80	valid
8.0ms	17×	body	320	valid
3.0ms	12×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
2	15
1	12
0	8

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (cos y) z (* x (sin y)))
0.1b	(* x (sin y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma (cos y) z (* x (sin y)))
13.0ms	(* x (sin y))

series186.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(fma (cos y) z (* x (sin y)))
50.0ms	(* x (sin y))

simplify2.2s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
4	2388
3	737
2	253
1	107
0	56

prune249.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (sin y) (* z (cos y)))
0.1b	(* z (cos y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma x (sin y) (* z (cos y)))
7.0ms	(* z (cos y))

series131.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(fma x (sin y) (* z (cos y)))
40.0ms	(* z (cos y))

simplify3.8s

Counts

36 → 36

Iterations

Iter	Nodes
done	5005
4	2119
3	611
2	210
1	90
0	49

prune324.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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:

11.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))

series708.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
149.0ms	(cbrt (cos y))
153.0ms	(cbrt (cos y))
174.0ms	(cbrt (cos y))

simplify4.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	4766
3	1197
2	374
1	149
0	68

prune650.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`prod-exp`
14×	`associate-r`
13×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
8×	`cbrt-unprod`
7×	`associate-l`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`swap-sqr` `*-commutative`
2×	`pow-to-exp` `unpow-prod-down` `unpow1/3` `pow-prod-down` `sqr-pow`
1×	`pow2` `sqr-cos` `pow-plus` `pow1/3` `pow-sqr` `cos-mult` `pow-prod-up`

Counts

4 → 95

Calls

4 calls:

15.0ms	(* z (pow (* (cos y) (cos y)) 1/3))
67.0ms	(* (* z (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
16.0ms	(* (cos y) (cos y))
2.0ms	(cbrt (cos y))

series397.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* z (pow (* (cos y) (cos y)) 1/3))
59.0ms	(* (* z (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
32.0ms	(* (cos y) (cos y))
155.0ms	(cbrt (cos y))

simplify3.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
3	3686
2	1018
1	347
0	135

prune773.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes365.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1545×	body	1280	valid
936.0ms	4242×	body	80	valid
820.0ms	1234×	body	640	valid
308.0ms	665×	body	320	valid
77.0ms	314×	body	160	valid