Details

sample51.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
7.0ms	19×	body	1280	valid
6.0ms	18×	body	2560	valid
3.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	30
1	24
0	12

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.9b	(+ (hypot re im) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
4.0ms	(+ (hypot re im) re)

series428.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(hypot re im)
264.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
91.0ms	(+ (hypot re im) re)

simplify2.0s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	3673
2	612
1	187
0	86

prune350.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ re (hypot re im)))
0.9b	(+ re (hypot re im))
0.9b	(+ re (hypot re im))
0.9b	(+ re (hypot re im))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-def`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`cbrt-prod` `expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `log1p-expm1-u` `distribute-lft-out`
3×	`+-commutative` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 67

Calls

4 calls:

6.0ms	(cbrt (+ re (hypot re im)))
9.0ms	(+ re (hypot re im))
9.0ms	(+ re (hypot re im))
10.0ms	(+ re (hypot re im))

series441.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt (+ re (hypot re im)))
97.0ms	(+ re (hypot re im))
63.0ms	(+ re (hypot re im))
73.0ms	(+ re (hypot re im))

simplify1.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	2969
2	566
1	184
0	82

prune597.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.4b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
23.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
21.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
18.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series475.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot re im)
261.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
74.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
80.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify893.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1169
1	291
0	129

prune497.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
10.6b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
26.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series579.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (hypot re im))
180.0ms	(cbrt (hypot re im))
160.0ms	(cbrt (hypot re im))
84.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify1.8s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	3151
2	523
1	151
0	63

prune415.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 13.3b

regimes315.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

821.0ms	6031×	body	80	valid
378.0ms	695×	body	2560	valid
231.0ms	300×	body	5120	valid
170.0ms	293×	body	640	valid
146.0ms	447×	body	1280	valid
34.0ms	151×	body	320	valid
9.0ms	83×	body	160	valid