Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
3.0ms	17×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	29	10
3	31	10
done	31	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.4b	(+ re (hypot re im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
3.0ms	(+ re (hypot re im))

series238.0ms

Counts

2 → 6

Calls

2 calls:

182.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
56.0ms	(+ re (hypot re im))

simplify2.5s

Counts

38 → 38

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	75	354
1	173	325
2	446	302
3	1277	293
4	3884	292
done	5001	292

prune99.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 11.3b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
9×	`add-cube-cbrt`
8×	`pow1`
7×	`associate-l`
6×	`associate-r`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ re (hypot re im)))
15.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
3.0ms	(+ re (hypot re im))

series351.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(sqrt (+ re (hypot re im)))
180.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
52.0ms	(+ re (hypot re im))

simplify1.6s

Counts

80 → 80

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	124	838
1	286	767
2	741	726
3	2024	715
done	5000	712

prune192.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 11.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
12.9b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt re)
0.0ms	(cbrt re)
0.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

series704.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt re)
174.0ms	(cbrt re)
179.0ms	(cbrt re)
177.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify1.2s

Counts

61 → 61

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	42	372
1	62	360
2	121	286
3	293	244
4	1040	244
done	5000	244

prune183.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt re))
0.6b	(cbrt (cbrt re))
0.6b	(cbrt (cbrt re))
12.8b	(fma (* (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (cbrt re)) (cbrt re) (hypot re im))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt (cbrt re))
1.0ms	(cbrt (cbrt re))
1.0ms	(cbrt (cbrt re))
0.0ms	(fma (* (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (cbrt re)) (cbrt re) (hypot re im))

series891.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt (cbrt re))
236.0ms	(cbrt (cbrt re))
242.0ms	(cbrt (cbrt re))
176.0ms	(fma (* (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (cbrt re)) (cbrt re) (hypot re im))

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	54	624
1	83	609
2	153	485
3	366	443
4	1263	443
done	5001	443

prune244.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.2b

regimes90.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample689.0ms

Algorithm

intervals

Results

210.0ms	5999×	body	80	valid
130.0ms	657×	body	2560	valid
84.0ms	524×	body	1280	valid
73.0ms	295×	body	5120	valid
39.0ms	308×	body	640	valid
13.0ms	142×	body	320	valid
5.0ms	75×	body	160	valid