Details

sample220.0ms

Algorithm

intervals

Results

39.0ms	15×	body	1280	valid
21.0ms	189×	body	80	valid
15.0ms	26×	body	2560	valid
5.0ms	14×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	3×	body	160	valid

simplify152.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (118.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	43	10
5	45	10
done	45	10

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

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

series558.0ms

Counts

2 → 6

Calls

2 calls:

435.0ms	(sqrt (* (- (hypot re im) re) 2.0))
123.0ms	(- (hypot re im) re)

simplify2.7s

Counts

49 → 49

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	107	626
1	235	523
2	751	446
3	4110	402
done	5000	402

prune230.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.7b

localize27.0ms

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))
16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite18.0ms

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:

3.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (hypot re im))
10.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series836.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (hypot re im))
134.0ms	(sqrt (hypot re im))
360.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
222.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify3.4s

Counts

65 → 65

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	93	753
1	201	559
2	741	486
3	4481	469
done	5000	469

prune408.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 14.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.3b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 129

Calls

4 calls:

5.0ms	(sqrt (sqrt (hypot re im)))
5.0ms	(sqrt (sqrt (hypot re im)))
54.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
1.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

series644.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (sqrt (hypot re im)))
159.0ms	(sqrt (sqrt (hypot re im)))
133.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
182.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

simplify1.4s

Counts

141 → 141

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	132	1875
1	286	1027
2	1380	942
done	5000	932

prune594.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 14.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
16.3b	(fma (sqrt (hypot re im)) (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (- re))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

20.0ms	(* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (- re))

series800.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
146.0ms	(cbrt (hypot re im))
161.0ms	(cbrt (hypot re im))
289.0ms	(fma (sqrt (hypot re im)) (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (- re))

simplify993.0ms

Counts

85 → 85

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	148	1367
1	323	1297
2	1312	1151
done	5000	1126

prune809.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 14.6b

regimes281.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	5998×	body	80	valid
375.0ms	726×	body	2560	valid
357.0ms	505×	body	1280	valid
166.0ms	299×	body	5120	valid
78.0ms	277×	body	640	valid
25.0ms	122×	body	320	valid
10.0ms	73×	body	160	valid