Details

sample84.0ms

Algorithm

intervals

Results

28.0ms	44×	body	1280	valid
19.0ms	45×	body	640	valid
14.0ms	136×	body	80	valid
6.0ms	17×	body	320	valid
3.0ms	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: 0.2b

localize50.0ms

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))

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	(* x (cos y))
9.0ms	(* z (sin y))

series204.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(- (* x (cos y)) (* z (sin y)))
64.0ms	(* x (cos y))
49.0ms	(* z (sin y))

simplify2.5s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	3626
2	639
1	202
0	91

prune445.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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))

rewrite38.0ms

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:

28.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))
2.0ms	(cbrt (cos y))

series656.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
132.0ms	(cbrt (cos y))
141.0ms	(cbrt (cos y))
121.0ms	(cbrt (cos y))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	640
1	152
0	68

prune646.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

11.0ms	(* z (sin y))
34.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
14.0ms	(* (cos y) (cos y))
1.0ms	(cbrt (cos y))

series268.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* z (sin y))
65.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
38.0ms	(* (cos y) (cos y))
107.0ms	(cbrt (cos y))

simplify1.6s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	2194
1	359
0	142

prune615.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (sin y))
0.2b	(* (* x (pow (+ 1/2 (* (cos (+ y y)) 1/2)) 1/3)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.4b	(+ 1/2 (* (cos (+ y y)) 1/2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-cbrt-cube` `add-cube-cbrt`
9×	`associate-r`
8×	`pow1` `prod-exp`
6×	`cbrt-prod` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`fma-def`
2×	`pow-prod-down` `*-commutative`
1×	`pow-to-exp` `+-commutative` `sum-log` `flip3-+` `distribute-rgt-out` `unpow1/3` `pow1/3` `distribute-rgt1-in` `pow-exp` `flip-+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

11.0ms	(* z (sin y))
74.0ms	(* (* x (pow (+ 1/2 (* (cos (+ y y)) 1/2)) 1/3)) (cbrt (cos y)))
2.0ms	(cbrt (cos y))
10.0ms	(+ 1/2 (* (cos (+ y y)) 1/2))

series499.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* z (sin y))
234.0ms	(* (* x (pow (+ 1/2 (* (cos (+ y y)) 1/2)) 1/3)) (cbrt (cos y)))
174.0ms	(cbrt (cos y))
39.0ms	(+ 1/2 (* (cos (+ y y)) 1/2))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1482
1	356
0	141

prune698.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes428.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	1481×	body	1280	valid
1.0s	4303×	body	80	valid
698.0ms	1303×	body	640	valid
346.0ms	632×	body	320	valid
63.0ms	281×	body	160	valid