Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	16×	body	2560	valid
3.0ms	12×	body	5120	valid
1.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8
done	46	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sqrt (+ (* re re) (* im im))) re)
30.3b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
16×	`sqrt-prod`
6×	`fma-neg`
4×	`add-log-exp`
3×	`pow1`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

2 → 59

Calls

2 calls:

51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify105.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	211	590
1	687	366
2	3279	321
3	5001	295
done	5001	295

prune138.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.8b	(- (* 1 (hypot re im)) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `prod-diff`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `hypot-udef` `flip3--` `fma-neg` `diff-log` `flip--` `distribute-lft-out--`

Counts

2 → 29

Calls

2 calls:

0.0ms	(hypot re im)
9.0ms	(- (* 1 (hypot re im)) re)

series108.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(hypot re im)
61.0ms	(- (* 1 (hypot re im)) re)

simplify50.0ms

Counts

35 → 35

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	134	133
1	388	100
2	1779	97
3	5002	95
done	5002	95

prune97.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

localize11.0ms

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)))
10.3b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
14×	`*-un-lft-identity`
13×	`add-cube-cbrt`
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×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
13.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
34.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series203.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot re im)
46.0ms	(hypot re im)
50.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
58.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify42.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	211	391
1	869	298
2	5001	281
done	5001	281

prune233.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.3b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
10.3b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
10.3b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`pow1`
18×	`*-un-lft-identity` `sqrt-prod`
15×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`prod-diff`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `pow-sqr` `flip--` `distribute-lft-out--`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

13.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
32.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
33.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
34.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series230.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
58.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
60.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
61.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify44.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	201	697
1	856	482
2	5001	445
done	5001	445

prune337.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes137.0ms

Accuracy

27.4% (4.6b remaining)

Error of 11.7b against oracle of 7.1b and baseline of 13.4b

bsearch45.0ms

Steps

Iters	Range		Point
8	7.746243714250649e-84	2.4297972203424506e-80	1.2775945728899134e-80

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	32	13
2	32	13
done	32	13

end0.0ms

sample763.0ms

Algorithm

intervals

Results

226.0ms	6006×	body	80	valid
143.0ms	691×	body	2560	valid
83.0ms	485×	body	1280	valid
72.0ms	291×	body	5120	valid
36.0ms	273×	body	640	valid
16.0ms	158×	body	320	valid
6.0ms	96×	body	160	valid