Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
5.0ms	23×	body	2560	valid
3.0ms	5×	body	640	valid
2.0ms	15×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	29	10
3	31	10
done	31	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.9b	(+ re (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `hypot-udef` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
3.0ms	(+ re (hypot re im))

series99.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(hypot re im)
56.0ms	(+ re (hypot re im))

simplify1.3s

Counts

33 → 33

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	42	193
1	89	179
2	156	169
3	310	169
4	715	169
5	2049	169
done	5000	169

prune92.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
7.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
2.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(hypot re im)
46.0ms	(hypot re im)
43.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
56.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify2.1s

Counts

99 → 99

Iterations

Useful iterations: 3 (432.0ms)

Iter	Nodes	Cost
0	87	990
1	168	533
2	463	501
3	2740	485
done	5000	485

prune226.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
7.5b	(+ re (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

5.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
0.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
2.0ms	(+ re (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
106.0ms	(cbrt (hypot re im))
104.0ms	(cbrt (hypot re im))
102.0ms	(+ re (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

simplify2.1s

Counts

78 → 78

Iterations

Useful iterations: 3 (648.0ms)

Iter	Nodes	Cost
0	129	1122
1	317	1052
2	1028	929
3	4641	898
done	5000	898

prune308.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
15.2b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt re)
0.0ms	(cbrt re)
0.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

series692.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt re)
173.0ms	(cbrt re)
170.0ms	(cbrt re)
174.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify778.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	42	372
1	62	360
2	121	286
3	309	244
4	1397	244
done	5001	244

prune186.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 13.6b

regimes113.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample684.0ms

Algorithm

intervals

Results

196.0ms	6020×	body	80	valid
145.0ms	694×	body	2560	valid
79.0ms	489×	body	1280	valid
72.0ms	294×	body	5120	valid
35.0ms	283×	body	640	valid
14.0ms	149×	body	320	valid
4.0ms	71×	body	160	valid