Details

sample52.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
11.0ms	24×	body	2560	valid
4.0ms	14×	body	1280	valid
3.0ms	6×	body	5120	valid
3.0ms	10×	body	640	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	29
1	24
0	12

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.7b	(+ (hypot re im) re)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

13.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
5.0ms	(+ (hypot re im) re)

series375.0ms

Counts

2 → 6

Calls

2 calls:

284.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
91.0ms	(+ (hypot re im) re)

simplify3.5s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
4	4675
3	1358
2	468
1	174
0	75

prune272.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series522.0ms

Counts

2 → 6

Calls

2 calls:

315.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
207.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify4.2s

Counts

29 → 29

Iterations

Iter	Nodes
done	5019
4	3291
3	1078
2	333
1	130
0	61

prune228.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series483.0ms

Counts

2 → 6

Calls

2 calls:

273.0ms	(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)

simplify4.3s

Counts

29 → 29

Iterations

Iter	Nodes
done	5019
4	3291
3	1078
2	333
1	130
0	61

prune230.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
0.4b	(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
31×	`sqrt-prod`
26×	`add-sqr-sqrt`
23×	`pow-prod-down`
20×	`pow1/2`
14×	`pow-prod-up`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`swap-sqr`
8×	`pow-sqr`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

4.0ms	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
32.0ms	(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series1.2s

Counts

4 → 12

Calls

4 calls:

357.0ms	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
381.0ms	(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
197.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
228.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.6s

Counts

124 → 124

Iterations

Iter	Nodes
done	5005
3	3680
2	1121
1	405
0	169

prune658.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.5b

regimes223.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

982.0ms	6038×	body	80	valid
246.0ms	697×	body	2560	valid
204.0ms	477×	body	1280	valid
157.0ms	285×	body	5120	valid
68.0ms	285×	body	640	valid
24.0ms	142×	body	320	valid
8.0ms	76×	body	160	valid