Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	200×	body	80	valid
3.0ms	18×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	14×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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:

8.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
6.0ms	(+ re (hypot re im))

series253.0ms

Counts

2 → 6

Calls

2 calls:

192.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
62.0ms	(+ re (hypot re im))

simplify2.9s

Counts

38 → 38

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	75	354
1	173	325
2	444	302
3	1193	293
4	3103	292
done	5000	292

prune98.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 11.9b

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))
0.7b	(+ re (hypot re im))

rewrite40.0ms

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:

7.0ms	(sqrt (+ re (hypot re im)))
25.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
6.0ms	(+ re (hypot re im))

series374.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(sqrt (+ re (hypot re im)))
190.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
60.0ms	(+ re (hypot re im))

simplify2.4s

Counts

80 → 80

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	124	838
1	285	767
2	725	726
3	1920	714
done	5000	712

prune181.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 11.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.2b	(* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0)))
0.3b	(* (* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(+ re (hypot re im))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

7.0ms	(sqrt (+ re (hypot re im)))
30.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0)))
59.0ms	(* (* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(+ re (hypot re im))

series615.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt (+ re (hypot re im)))
239.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0)))
186.0ms	(* (* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
59.0ms	(+ re (hypot re im))

simplify1.9s

Counts

119 → 119

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	171	1567
1	421	1320
2	1186	1214
3	3488	1199
done	5000	1195

prune286.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 11.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
13.5b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite4.0ms

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:

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

series732.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt re)
180.0ms	(cbrt re)
179.0ms	(cbrt re)
187.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify797.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	42	372
1	62	360
2	121	286
3	329	244
4	1216	244
done	5000	244

prune202.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 11.8b

regimes41.0ms

Accuracy

0% (0.2b remaining)

Error of 12.8b against oracle of 12.6b and baseline of 12.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (3.0ms)

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

end0.0ms

sample665.0ms

Algorithm

intervals

Results

182.0ms	6072×	body	80	valid
129.0ms	700×	body	2560	valid
75.0ms	507×	body	1280	valid
65.0ms	299×	body	5120	valid
29.0ms	232×	body	640	valid
10.0ms	123×	body	320	valid
4.0ms	67×	body	160	valid