Details

sample166.0ms

Algorithm

intervals

Results

19.0ms	199×	body	80	valid
10.0ms	19×	body	2560	valid
8.0ms	18×	body	1280	valid
5.0ms	8×	body	5120	valid
3.0ms	10×	body	640	valid
0.0ms	1×	body	160	valid
0.0ms	1×	body	320	valid

simplify95.0ms

Counts: 1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b	(- (hypot re im) re)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

Slowest

16.0ms	(sqrt (* (- (hypot re im) re) 2.0))
13.0ms	(- (hypot re im) re)
0.0ms	(hypot re im)

series418.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

269.0ms	(sqrt (* (- (hypot re im) re) 2.0))
97.0ms	(- (hypot re im) re)
51.0ms	(hypot re im)

simplify1.6s

Counts: 65 → 65

prune566.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.3b	(- (hypot re im) re)
0.0b	(sqrt (- (hypot re im) re))
0.0b	(hypot re im)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

Slowest

37.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
12.0ms	(sqrt (- (hypot re im) re))
10.0ms	(- (hypot re im) re)
6.0ms	(hypot re im)

series665.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

321.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
185.0ms	(sqrt (- (hypot re im) re))
84.0ms	(- (hypot re im) re)
75.0ms	(hypot re im)

simplify861.0ms

Counts: 109 → 109

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

localize23.0ms

Local error

Found 4 expressions with local error:

14.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))

rewrite12.0ms

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:

Slowest

6.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
2.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series819.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

342.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
210.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
135.0ms	(sqrt (hypot re im))
132.0ms	(sqrt (hypot re im))

simplify2.9s

Counts: 69 → 69

prune823.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.2b

localize29.0ms

Local error

Found 4 expressions with local error:

13.9b	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

Slowest

31.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
4.0ms	(sqrt (sqrt (hypot re im)))
4.0ms	(sqrt (sqrt (hypot re im)))
1.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series644.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))
165.0ms	(sqrt (sqrt (hypot re im)))
160.0ms	(sqrt (sqrt (hypot re im)))
132.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify1.8s

Counts: 145 → 145

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

regimes221.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch4.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1000.0ms	5991×	body	80	valid
935.0ms	706×	body	2560	valid
341.0ms	479×	body	1280	valid
291.0ms	308×	body	5120	valid
184.0ms	280×	body	640	valid
51.0ms	149×	body	320	valid
19.0ms	87×	body	160	valid