Details

sample96.0ms

Algorithm

intervals

Results

36.0ms	46×	body	1280	valid
19.0ms	42×	body	640	valid
13.0ms	132×	body	80	valid
9.0ms	15×	body	160	valid
7.0ms	21×	body	320	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

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:

49.0ms	(+ (* x (cos y)) (* z (sin y)))
18.0ms	(* x (cos y))
20.0ms	(* z (sin y))

series251.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(+ (* x (cos y)) (* z (sin y)))
76.0ms	(* x (cos y))
73.0ms	(* z (sin y))

simplify3.5s

Counts

63 → 63

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	87	494
1	196	449
2	503	417
3	1307	417
4	3735	417
done	5000	417

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

26.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
3.0ms	(cbrt (cos y))

series635.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
145.0ms	(cbrt (cos y))
123.0ms	(cbrt (cos y))
169.0ms	(cbrt (cos y))

simplify2.9s

Counts

93 → 93

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	68	726
1	128	651
2	353	551
3	1189	529
done	5000	520

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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:

18.0ms	(* z (sin y))
86.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series274.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* z (sin y))
54.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
19.0ms	(pow (cos y) 2)
156.0ms	(cbrt (cos y))

simplify3.9s

Counts

92 → 92

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	134	813
1	297	708
2	866	632
3	3395	571
done	5000	562

prune538.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (cbrt (cos y))))
0.2b	(pow (cos y) 2)
0.3b	(log1p (cbrt (cos y)))
0.3b	(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` `expm1-log1p-u`
4×	`add-cbrt-cube` `log1p-expm1-u` `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	(expm1 (log1p (cbrt (cos y))))
7.0ms	(pow (cos y) 2)
1.0ms	(log1p (cbrt (cos y)))
3.0ms	(cbrt (cos y))

series791.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(expm1 (log1p (cbrt (cos y))))
19.0ms	(pow (cos y) 2)
250.0ms	(log1p (cbrt (cos y)))
166.0ms	(cbrt (cos y))

simplify4.9s

Counts

67 → 67

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	85	437
1	148	373
2	294	336
3	768	329
4	4700	324
done	5000	324

prune410.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes251.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	20	19
done	20	19

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	1529×	body	1280	valid
683.0ms	4285×	body	80	valid
677.0ms	615×	body	320	valid
591.0ms	1232×	body	640	valid
95.0ms	339×	body	160	valid