Details

sample61.0ms

Algorithm

intervals

Results

15.0ms	193×	body	80	valid
12.0ms	24×	body	2560	valid
6.0ms	14×	body	1280	valid
4.0ms	6×	body	5120	valid
3.0ms	10×	body	640	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	30
1	24
0	12

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

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))
9.0ms	(+ (hypot re im) re)

series366.0ms

Counts

2 → 6

Calls

2 calls:

277.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
89.0ms	(+ (hypot re im) re)

simplify1.9s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
3	3748
2	604
1	174
0	75

prune288.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.5b

localize13.0ms

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)

rewrite4.0ms

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:

3.0ms	(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)

series479.0ms

Counts

2 → 6

Calls

2 calls:

304.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
175.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify3.6s

Counts

29 → 29

Iterations

Iter	Nodes
done	5000
3	2320
2	417
1	130
0	61

prune237.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
0.5b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

2.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
16.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series870.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
202.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
220.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
206.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	872
1	206
0	89

prune627.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))) (sqrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

35×	`sqrt-pow1`
34×	`pow1`
26×	`pow-prod-up`
19×	`pow1/2`
11×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cbrt-cube` `associate-r` `add-exp-log`
7×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow3` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `fma-udef`
2×	`pow-plus` `sqrt-unprod`
1×	`associate-l` `*-commutative`

Counts

4 → 75

Calls

4 calls:

50.0ms	(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))) (sqrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series842.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))) (sqrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
222.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
216.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
221.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.6s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1249
1	240
0	96

prune628.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.5b

regimes236.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

878.0ms	6038×	body	80	valid
367.0ms	697×	body	2560	valid
279.0ms	477×	body	1280	valid
144.0ms	285×	body	5120	valid
124.0ms	285×	body	640	valid
28.0ms	142×	body	320	valid
10.0ms	76×	body	160	valid