Details

sample146.0ms

Algorithm

intervals

Results

17.0ms	203×	body	80	valid
8.0ms	15×	body	2560	valid
6.0ms	16×	body	1280	valid
5.0ms	9×	body	5120	valid
2.0ms	7×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(- (hypot re im) re)
0.2b	(sqrt (* (- (hypot re im) re) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 45

Calls

2 calls:

5.0ms	(- (hypot re im) re)
9.0ms	(sqrt (* (- (hypot re im) re) 2.0))

series501.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (hypot re im) re)
437.0ms	(sqrt (* (- (hypot re im) re) 2.0))

simplify1.6s

Counts

51 → 51

Iterations

Iter	Nodes
done	2000
4	2000
3	1642
2	528
1	237
0	109

prune263.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.1b	(- (hypot re im) re)
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `associate-l`
6×	`associate-r`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 86

Calls

3 calls:

6.0ms	(sqrt (- (hypot re im) re))
5.0ms	(- (hypot re im) re)
20.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

series550.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(sqrt (- (hypot re im) re))
73.0ms	(- (hypot re im) re)
300.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))

simplify1.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	2001
3	2001
2	873
1	364
0	162

prune395.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.2b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
12.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 57

Calls

4 calls:

2.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))
8.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series869.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (hypot re im))
135.0ms	(sqrt (hypot re im))
368.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
239.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify949.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2001
3	2001
2	565
1	207
0	97

prune387.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.2b	(sqrt (* (fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re)) 2.0))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
12.9b	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

77×	`sqrt-prod`
50×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`pow1`
19×	`pow1/2`
18×	`*-un-lft-identity` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
5×	`pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 125

Calls

4 calls:

3.0ms	(sqrt (sqrt (hypot re im)))
8.0ms	(sqrt (* (fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re)) 2.0))
24.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
1.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series768.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt (sqrt (hypot re im)))
300.0ms	(sqrt (* (fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re)) 2.0))
105.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
189.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify1.1s

Counts

137 → 137

Iterations

Iter	Nodes
done	2000
3	2000
2	842
1	367
0	172

prune567.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.4b

regimes144.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	6047×	body	80	valid
517.0ms	690×	body	2560	valid
335.0ms	492×	body	1280	valid
266.0ms	286×	body	5120	valid
172.0ms	273×	body	640	valid
45.0ms	136×	body	320	valid
16.0ms	76×	body	160	valid