Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	190×	body	80	valid
5.0ms	23×	body	2560	valid
3.0ms	13×	body	5120	valid
2.0ms	14×	body	1280	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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: 12.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.6b	(+ 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:

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

series250.0ms

Counts

2 → 6

Calls

2 calls:

195.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
55.0ms	(+ re (hypot re im))

simplify2.5s

Counts

38 → 38

Iterations

Useful iterations: 4 (1.7s)

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

prune101.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.3b

localize9.0ms

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))
0.6b	(+ re (hypot re im))

rewrite22.0ms

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)))
13.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
3.0ms	(+ re (hypot re im))

series365.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(sqrt (+ re (hypot re im)))
187.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
58.0ms	(+ 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

prune193.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 12.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.3b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
0.6b	(+ re (hypot re im))
3.8b	(exp (log (* (sqrt (+ re (hypot re im))) (sqrt 2.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(sqrt (+ re (hypot re im)))
14.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
2.0ms	(+ re (hypot re im))
22.0ms	(exp (log (* (sqrt (+ re (hypot re im))) (sqrt 2.0))))

series547.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (+ re (hypot re im)))
183.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
57.0ms	(+ re (hypot re im))
185.0ms	(exp (log (* (sqrt (+ re (hypot re im))) (sqrt 2.0))))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	153	1151
1	325	1018
2	806	963
3	2154	943
done	5000	939

prune286.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 12.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
15.6b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite3.0ms

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))

series698.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt re)
177.0ms	(cbrt re)
173.0ms	(cbrt re)
177.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify1.2s

Counts

61 → 61

Iterations

Useful iterations: 3 (41.0ms)

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

prune179.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 12.3b

regimes75.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.2b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample706.0ms

Algorithm

intervals

Results

208.0ms	5999×	body	80	valid
142.0ms	699×	body	2560	valid
83.0ms	478×	body	1280	valid
78.0ms	310×	body	5120	valid
37.0ms	288×	body	640	valid
15.0ms	151×	body	320	valid
5.0ms	75×	body	160	valid