Details

sample144.0ms

Algorithm

intervals

Results

18.0ms	195×	body	80	valid
8.0ms	13×	body	5120	valid
8.0ms	16×	body	2560	valid
4.0ms	9×	body	1280	valid
2.0ms	9×	body	320	valid
2.0ms	6×	body	640	valid
1.0ms	8×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	42
3	35
2	27
1	19
0	12

prune52.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
2.3b	(- (hypot re im) re)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`hypot-udef` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

0.0ms	(hypot re im)
14.0ms	(- (hypot re im) re)

series209.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(hypot re im)
122.0ms	(- (hypot re im) re)

simplify3.3s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
5	4501
4	1608
3	663
2	260
1	140
0	69

prune213.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.6b

localize25.0ms

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)))
10.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
20.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
12.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series357.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(hypot re im)
86.0ms	(hypot re im)
83.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
107.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
3	1378
2	512
1	223
0	108

prune542.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 12.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
10.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
10.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-log-exp`
9×	`prod-diff`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `pow-sqr` `flip--` `difference-of-squares`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

11.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
11.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
23.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
11.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series345.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
75.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
110.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
93.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify2.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5002
3	1378
2	507
1	214
0	101

prune817.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 12.5b

localize121.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
10.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
10.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
12.5b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-log-exp`
9×	`prod-diff`
8×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-prod` `sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`
2×	`difference-of-squares`
1×	`pow1/3`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
17.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
12.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
32.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series442.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (hypot re im))
92.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
81.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
79.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify2.8s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
4	4104
3	1319
2	514
1	250
0	108

prune810.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 12.5b

regimes322.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

943.0ms	6073×	body	80	valid
488.0ms	665×	body	2560	valid
164.0ms	467×	body	1280	valid
150.0ms	300×	body	5120	valid
127.0ms	276×	body	640	valid
26.0ms	129×	body	320	valid
11.0ms	90×	body	160	valid