Details

sample50.0ms

Algorithm

intervals

Results

11.0ms	197×	body	80	valid
10.0ms	15×	body	640	valid
6.0ms	18×	body	2560	valid
3.0ms	7×	body	5120	valid
2.0ms	9×	body	1280	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
9.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
7.0ms	(+ re (hypot re im))

series451.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(hypot re im)
272.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
95.0ms	(+ re (hypot re im))

simplify5.3s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.5s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1219	345
4	3260	344
done	5001	344

prune245.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.0b	(hypot re im)
0.4b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
0.7b	(+ re (hypot re im))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

16.0ms	(sqrt (+ re (hypot re im)))
1.0ms	(hypot re im)
52.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
12.0ms	(+ re (hypot re im))

series680.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(sqrt (+ re (hypot re im)))
89.0ms	(hypot re im)
298.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
85.0ms	(+ re (hypot re im))

simplify3.9s

Counts

93 → 93

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	135	898
1	298	819
2	742	778
3	1970	766
done	5000	764

prune339.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.3b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

0.0ms	(hypot re im)
85.0ms	(* (* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
63.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0)))
6.0ms	(+ re (hypot re im))

series802.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot re im)
300.0ms	(* (* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
365.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (sqrt 2.0)))
84.0ms	(+ re (hypot re im))

simplify2.9s

Counts

110 → 110

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	157	1408
1	375	1181
2	1087	1086
3	3349	1074
done	5000	1071

prune531.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.3b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
8.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
6.0ms	(+ re (hypot re im))

series500.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(hypot re im)
314.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
105.0ms	(+ re (hypot re im))

simplify4.7s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1219	345
4	3260	344
done	5001	344

prune222.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.3b

regimes98.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.2b 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

sample2.2s

Algorithm

intervals

Results

900.0ms	6004×	body	80	valid
429.0ms	690×	body	2560	valid
278.0ms	474×	body	1280	valid
153.0ms	310×	body	5120	valid
73.0ms	295×	body	640	valid
29.0ms	151×	body	320	valid
13.0ms	76×	body	160	valid