Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
5.0ms	18×	body	2560	valid
4.0ms	18×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	10×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify30.0ms

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.4b	(+ re (hypot re im))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
7.0ms	(+ re (hypot re im))

series139.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(hypot re im)
68.0ms	(+ re (hypot re im))

simplify5.2s

Counts

33 → 33

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	42	193
1	89	179
2	178	169
3	352	169
4	917	169
5	2217	169
done	5000	169

prune169.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.5b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
1.0ms	(hypot re im)
34.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
12.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(hypot re im)
83.0ms	(hypot re im)
64.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
86.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify5.2s

Counts

99 → 99

Iterations

Useful iterations: 4 (3.0s)

Iter	Nodes	Cost
0	87	990
1	166	533
2	409	501
3	1155	485
4	4248	471
done	5000	471

prune350.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
19×	`pow1`
14×	`add-cube-cbrt`
12×	`sqrt-div`
11×	`swap-sqr`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-r/` `associate-l/` `sum-log`
1×	`pow2` `hypot-udef` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

1.0ms	(hypot re im)
46.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
18.0ms	(+ (hypot re im) re)
11.0ms	(+ (hypot re im) re)

series306.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot re im)
76.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
100.0ms	(+ (hypot re im) re)
70.0ms	(+ (hypot re im) re)

simplify5.0s

Counts

120 → 120

Iterations

Useful iterations: 4 (3.3s)

Iter	Nodes	Cost
0	103	1514
1	179	1004
2	441	926
3	1213	889
4	4266	865
done	5000	865

prune515.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (+ (hypot re im) re)))
0.4b	(+ (hypot re im) re)
15.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

1.0ms	(hypot re im)
37.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (+ (hypot re im) re)))
6.0ms	(+ (hypot re im) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series1.1s

Counts

4 → 12

Calls

4 calls:

87.0ms	(hypot re im)
738.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (+ (hypot re im) re)))
75.0ms	(+ (hypot re im) re)
206.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.3s

Counts

84 → 84

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	135	1260
1	290	793
2	799	672
3	2415	638
done	5001	634

prune400.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.5b

regimes139.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	18
1	14	18
done	14	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

942.0ms	6028×	body	80	valid
391.0ms	692×	body	2560	valid
190.0ms	283×	body	5120	valid
188.0ms	483×	body	1280	valid
131.0ms	288×	body	640	valid
29.0ms	151×	body	320	valid
10.0ms	75×	body	160	valid