Details

sample122.0ms

Algorithm

intervals

Results

44.0ms	49×	body	1280	valid
24.0ms	40×	body	640	valid
17.0ms	140×	body	80	valid
5.0ms	13×	body	320	valid
4.0ms	14×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	25
3	25
2	21
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

3 → 56

Calls

3 calls:

11.0ms	(- (* x (cos y)) (* z (sin y)))
7.0ms	(* z (sin y))
8.0ms	(* x (cos y))

series253.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(- (* x (cos y)) (* z (sin y)))
76.0ms	(* z (sin y))
67.0ms	(* x (cos y))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5003
3	1692
2	489
1	200
0	91

prune428.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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:

1.0ms	(fma x (cos y) (- (* z (sin y))))
15.0ms	(* z (sin y))

series191.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(fma x (cos y) (- (* z (sin y))))
59.0ms	(* z (sin y))

simplify2.1s

Counts

36 → 36

Iterations

Iter	Nodes
done	5007
4	2043
3	604
2	208
1	93
0	49

prune268.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

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))

rewrite27.0ms

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:

19.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))

series601.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
123.0ms	(cbrt (cos y))
140.0ms	(cbrt (cos y))
155.0ms	(cbrt (cos y))

simplify4.1s

Counts

93 → 93

Iterations

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

prune647.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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:

16.0ms	(* x (pow (* (cos y) (cos y)) 1/3))
55.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
16.0ms	(* (cos y) (cos y))
2.0ms	(cbrt (cos y))

series408.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* x (pow (* (cos y) (cos y)) 1/3))
67.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
30.0ms	(* (cos y) (cos y))
180.0ms	(cbrt (cos y))

simplify3.0s

Counts

107 → 107

Iterations

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

prune763.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes881.0ms

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	18
1	18
0	15

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	1491×	body	1280	valid
1.2s	1300×	body	640	valid
589.0ms	4233×	body	80	valid
369.0ms	643×	body	320	valid
135.0ms	333×	body	160	valid