Details

sample52.0ms

Algorithm

intervals

Results

20.0ms	195×	body	80	valid
6.0ms	20×	body	2560	valid
4.0ms	13×	body	1280	valid
4.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

1.0ms	(hypot re im)
17.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
13.0ms	(+ re (hypot re im))

series421.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(hypot re im)
249.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
107.0ms	(+ re (hypot re im))

simplify4.8s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1219	345
4	3260	344
done	5001	344

prune175.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.6b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

3.0ms	(sqrt (hypot re im))
14.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
25.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
11.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (hypot re im))
236.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
50.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
79.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify2.9s

Counts

109 → 109

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	143	1359
1	308	755
2	807	698
3	2369	668
done	5000	658

prune462.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.3b	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
0.8b	(pow (sqrt (sqrt (hypot re im))) 3)
11.7b	(+ re (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `unswap-sqr`
10×	`pow1` `add-exp-log`
9×	`associate-r`
8×	`sqrt-pow1`
7×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `pow-exp`
1×	`+-commutative` `flip3-+` `pow-plus` `sum-log` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `flip-+` `rem-cube-cbrt`

Counts

4 → 152

Calls

4 calls:

5.0ms	(sqrt (sqrt (hypot re im)))
44.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
5.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
7.0ms	(+ re (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (sqrt (hypot re im)))
54.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
222.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
66.0ms	(+ re (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))))

simplify1.4s

Counts

164 → 164

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	153	2492
1	364	1674
2	1179	1451
done	5000	1307

prune574.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (sqrt (hypot re im))))
0.6b	(cbrt (sqrt (hypot re im)))
0.8b	(pow (sqrt (sqrt (hypot re im))) 3)
11.3b	(+ re (* (* (pow (sqrt (sqrt (hypot re im))) 3) (cbrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-prod`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`cbrt-prod`
9×	`unpow-prod-down` `cube-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`pow1/2` `pow1/3`
1×	`+-commutative` `cube-mult` `pow-to-exp` `flip3-+` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

3.0ms	(cbrt (sqrt (sqrt (hypot re im))))
2.0ms	(cbrt (sqrt (hypot re im)))
11.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
13.0ms	(+ re (* (* (pow (sqrt (sqrt (hypot re im))) 3) (cbrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (sqrt (sqrt (hypot re im))))
187.0ms	(cbrt (sqrt (hypot re im)))
180.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
89.0ms	(+ re (* (* (pow (sqrt (sqrt (hypot re im))) 3) (cbrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	161	1408
1	365	1211
2	979	944
done	5000	848

prune456.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.1b

regimes188.0ms

Accuracy

0% (1.9b remaining)

Error of 15.8b against oracle of 13.9b and baseline of 15.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	22	25
done	22	25

end0.0ms

sample2.1s

Algorithm

intervals

Results

787.0ms	707×	body	2560	valid
522.0ms	5940×	body	80	valid
184.0ms	542×	body	1280	valid
165.0ms	255×	body	5120	valid
126.0ms	301×	body	640	valid
31.0ms	166×	body	320	valid
12.0ms	89×	body	160	valid