Details

sample384.0ms

Algorithm

intervals

Results

87.0ms	29×	body	2560	valid
33.0ms	176×	body	80	valid
20.0ms	20×	body	1280	valid
13.0ms	11×	body	5120	valid
8.0ms	11×	body	640	valid
2.0ms	7×	body	160	valid
1.0ms	2×	body	320	valid

simplify138.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
1.5b	(- (hypot re im) re)

rewrite43.0ms

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

Counts

3 → 53

Calls

3 calls:

15.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
13.0ms	(- (hypot re im) re)

series506.0ms

Counts

3 → 9

Calls

3 calls:

307.0ms	(sqrt (* (- (hypot re im) re) 2.0))
94.0ms	(hypot re im)
105.0ms	(- (hypot re im) re)

simplify2.2s

Counts

62 → 62

Iterations

Iter	Nodes
4	5402
3	1625
2	511
1	229
0	115

prune600.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.9b

localize39.0ms

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)))
10.5b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
13×	`*-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×	`prod-diff` `pow-sqr`
2×	`flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`pow2` `hypot-udef` `sub-neg` `rem-square-sqrt` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

0.0ms	(hypot re im)
14.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
8.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
23.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series923.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(hypot re im)
689.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
64.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
82.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify657.0ms

Counts

107 → 107

Iterations

Iter	Nodes
3	2014
2	755
1	313
0	152

prune916.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
10.1b	(- (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`associate-r` `prod-diff`
2×	`pow1/3` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 68

Calls

4 calls:

10.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
27.0ms	(- (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

series570.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
143.0ms	(cbrt (hypot re im))
154.0ms	(cbrt (hypot re im))
140.0ms	(- (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

simplify1.6s

Counts

80 → 80

Iterations

Iter	Nodes
3	3030
2	962
1	352
0	147

prune1.0s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 16.8b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.6b	(cbrt (hypot re im))
14.0b	(- (* (* (sqrt (hypot re im)) (fabs (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) (sqrt (cbrt (hypot re im)))) re)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

49×	`cbrt-prod`
42×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`pow1/3`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`prod-diff`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `fma-neg` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 105

Calls

4 calls:

1.0ms	(cbrt (sqrt (hypot re im)))
9.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
20.0ms	(- (* (* (sqrt (hypot re im)) (fabs (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) (sqrt (cbrt (hypot re im)))) re)

series640.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (sqrt (hypot re im)))
160.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
180.0ms	(cbrt (hypot re im))
143.0ms	(- (* (* (sqrt (hypot re im)) (fabs (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) (sqrt (cbrt (hypot re im)))) re)

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
3	2666
2	911
1	353
0	163

prune1.8s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 16.8b

regimes246.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	6054×	body	80	valid
637.0ms	673×	body	2560	valid
392.0ms	510×	body	1280	valid
348.0ms	271×	body	5120	valid
141.0ms	283×	body	640	valid
53.0ms	132×	body	320	valid
19.0ms	77×	body	160	valid