Details

sample220.0ms

Algorithm

intervals

Results

34.0ms	195×	body	80	valid
19.0ms	18×	body	2560	valid
13.0ms	11×	body	5120	valid
11.0ms	15×	body	1280	valid
6.0ms	9×	body	640	valid
3.0ms	6×	body	320	valid
1.0ms	2×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.6b	(- (hypot re im) re)

rewrite41.0ms

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:

0.0ms	(hypot re im)
15.0ms	(sqrt (* (- (hypot re im) re) 2.0))
24.0ms	(- (hypot re im) re)

series414.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(hypot re im)
252.0ms	(sqrt (* (- (hypot re im) re) 2.0))
88.0ms	(- (hypot re im) re)

simplify2.5s

Counts

65 → 65

Iterations

Iter	Nodes
4	5254
3	1657
2	521
1	233
0	118

prune649.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
0.4b	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `sqrt-prod`
28×	`sqrt-div`
27×	`add-cube-cbrt`
23×	`pow-prod-down`
20×	`pow1/2`
18×	`prod-diff`
16×	`associate-*l/`
14×	`pow-prod-up`
9×	`flip3--` `swap-sqr` `flip--`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 162

Calls

4 calls:

7.0ms	(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
89.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
11.0ms	(- (hypot re im) re)
11.0ms	(- (hypot re im) re)

series767.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
249.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
79.0ms	(- (hypot re im) re)
97.0ms	(- (hypot re im) re)

simplify1.7s

Counts

174 → 174

Iterations

Iter	Nodes
3	3581
2	1149
1	463
0	220

prune2.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (- (hypot re im) re)))) (sqrt (sqrt 2.0)))
0.3b	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (- (hypot re im) re))))
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)

rewrite734.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-div`
44×	`add-sqr-sqrt`
36×	`sqrt-prod`
32×	`*-un-lft-identity`
30×	`sqrt-pow1`
28×	`pow1`
26×	`add-cube-cbrt`
24×	`associate-*l/`
21×	`pow-prod-down`
20×	`associate-r`
18×	`prod-diff`
14×	`flip3--` `flip--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1/2`
8×	`frac-times` `associate-l` `add-log-exp`
6×	`fma-neg` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `associate-*r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `diff-log` `*-commutative`

Counts

4 → 151

Calls

4 calls:

663.0ms	(* (* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (- (hypot re im) re)))) (sqrt (sqrt 2.0)))
49.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (- (hypot re im) re))))
6.0ms	(- (hypot re im) re)
11.0ms	(- (hypot re im) re)

series769.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (- (hypot re im) re)))) (sqrt (sqrt 2.0)))
354.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (- (hypot re im) re))))
70.0ms	(- (hypot re im) re)
100.0ms	(- (hypot re im) re)

simplify2.2s

Counts

163 → 163

Iterations

Iter	Nodes
3	4951
2	1502
1	532
0	237

prune2.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

6.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
6.0ms	(- (hypot re im) re)

series352.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (hypot re im) re)
105.0ms	(- (hypot re im) re)
85.0ms	(- (hypot re im) re)
93.0ms	(- (hypot re im) re)

simplify3.9s

Counts

128 → 128

Iterations

Iter	Nodes
5	6504
4	1902
3	694
2	225
1	117
0	62

prune2.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.3b

regimes256.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	6035×	body	80	valid
732.0ms	701×	body	2560	valid
426.0ms	463×	body	1280	valid
280.0ms	276×	body	5120	valid
160.0ms	284×	body	640	valid
53.0ms	135×	body	320	valid
31.0ms	106×	body	160	valid