Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	28×	body	2560	valid
7.0ms	193×	body	80	valid
2.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	35	10
4	41	10
5	43	10
done	43	10

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.5b	(- (hypot re im) re)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*l/` `flip--`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

0.0ms	(hypot re im)
4.0ms	(sqrt (* (- (hypot re im) re) 2.0))
3.0ms	(- (hypot re im) re)

series286.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(hypot re im)
179.0ms	(sqrt (* (- (hypot re im) re) 2.0))
61.0ms	(- (hypot re im) re)

simplify1.2s

Counts

62 → 62

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	115	686
1	232	572
2	557	498
3	1951	452
done	5001	451

prune158.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (- (hypot re im) re))
0.3b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.5b	(- (hypot re im) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
17×	`sqrt-prod`
16×	`add-cube-cbrt`
9×	`pow1` `prod-diff`
8×	`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×	`flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`sub-neg` `rem-sqrt-square` `hypot-udef` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

0.0ms	(hypot re im)
8.0ms	(sqrt (- (hypot re im) re))
14.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
3.0ms	(- (hypot re im) re)

series413.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot re im)
128.0ms	(sqrt (- (hypot re im) re))
181.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
55.0ms	(- (hypot re im) re)

simplify1.4s

Counts

105 → 105

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	168	1199
1	351	1045
2	868	953
3	2725	903
done	5000	902

prune250.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series571.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (hypot re im))
91.0ms	(sqrt (hypot re im))
246.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
145.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.1s

Counts

65 → 65

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	93	753
1	201	559
2	559	486
3	1915	467
done	5001	466

prune194.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 12.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
15.5b	(fma (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (sqrt (hypot re im)) (- re))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 64

Calls

4 calls:

6.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
0.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series510.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
109.0ms	(cbrt (hypot re im))
110.0ms	(cbrt (hypot re im))
163.0ms	(fma (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify1.6s

Counts

76 → 76

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	136	1064
1	293	1015
2	883	917
3	3092	886
done	5001	882

prune309.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 12.9b

regimes136.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample688.0ms

Algorithm

intervals

Results

203.0ms	6026×	body	80	valid
149.0ms	713×	body	2560	valid
78.0ms	481×	body	1280	valid
72.0ms	294×	body	5120	valid
36.0ms	266×	body	640	valid
14.0ms	144×	body	320	valid
5.0ms	76×	body	160	valid