Details

sample185.0ms

Algorithm

intervals

Results

25.0ms	190×	body	80	valid
15.0ms	21×	body	2560	valid
10.0ms	19×	body	1280	valid
8.0ms	10×	body	5120	valid
4.0ms	7×	body	640	valid
2.0ms	6×	body	160	valid
1.0ms	3×	body	320	valid

simplify64.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	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: 14.1b

localize17.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`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

1 → 29

Calls

1 calls:

7.0ms

(- (hypot re im) re)

series264.0ms

Counts

1 → 3

Calls

1 calls:

264.0ms

(- (hypot re im) re)

simplify2.1s

Counts

32 → 32

Iterations

Iter	Nodes
done	2000
5	2000
4	1936
3	709
2	251
1	131
0	62

prune364.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.9b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

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

series475.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(sqrt (hypot re im))
141.0ms	(sqrt (hypot re im))
197.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.2s

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
4	2001
3	1008
2	299
1	122
0	61

prune657.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.0b	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

rewrite37.0ms

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:

2.0ms	(sqrt (sqrt (hypot re im)))
7.0ms	(sqrt (sqrt (hypot re im)))
25.0ms	(* (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))

series658.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (sqrt (hypot re im)))
164.0ms	(sqrt (sqrt (hypot re im)))
127.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
198.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify1.1s

Counts

145 → 145

Iterations

Iter	Nodes
done	2010
4	2010
3	1547
2	587
1	282
0	136

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
0.6b	(cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
16.0b	(fma (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (sqrt (hypot re im)) (- re))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `sqrt-prod`
18×	`pow1` `associate-l`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`sqrt-pow1`
10×	`associate-r`
9×	`unswap-sqr`
8×	`pow1/2` `add-exp-log`
7×	`add-cbrt-cube`
6×	`pow-prod-up`
4×	`expm1-log1p-u` `cube-unmult` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `pow-plus` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`
1×	`pow1/3` `sqrt-unprod` `fma-udef`

Counts

4 → 103

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
29.0ms	(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
6.0ms	(cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
0.0ms	(fma (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (sqrt (hypot re im)) (- re))

series656.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
113.0ms	(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
147.0ms	(cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
171.0ms	(fma (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (sqrt (hypot re im)) (- re))

simplify1.0s

Counts

115 → 115

Iterations

Iter	Nodes
done	2000
3	2000
2	860
1	335
0	155

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.9b

regimes196.0ms

Accuracy

0% (0.2b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

802.0ms	6107×	body	80	valid
554.0ms	664×	body	2560	valid
268.0ms	459×	body	1280	valid
259.0ms	297×	body	5120	valid
126.0ms	251×	body	640	valid
81.0ms	135×	body	320	valid
44.0ms	87×	body	160	valid