Details

sample57.0ms

Algorithm

intervals

Results

16.0ms	201×	body	80	valid
6.0ms	13×	body	2560	valid
6.0ms	16×	body	1280	valid
4.0ms	12×	body	640	valid
4.0ms	7×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.0b	(hypot re im)
1.1b	(+ re (hypot re im))

rewrite53.0ms

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:

40.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
1.0ms	(hypot re im)
10.0ms	(+ re (hypot re im))

series882.0ms

Counts

3 → 9

Calls

3 calls:

328.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
447.0ms	(hypot re im)
107.0ms	(+ re (hypot re im))

simplify4.7s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	459	354
3	1221	345
4	3261	344
done	5001	344

prune256.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))
6.5b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1`
9×	`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` `hypot-udef` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

0.0ms	(hypot re im)
18.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
25.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
12.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(hypot re im)
277.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
90.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
89.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	129	1271
1	260	679
2	684	634
3	2064	608
done	5000	597

prune349.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
7.7b	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

18.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
2.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
12.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
158.0ms	(cbrt (hypot re im))
184.0ms	(cbrt (hypot re im))
160.0ms	(+ re (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

simplify3.5s

Counts

78 → 78

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	132	1125
1	321	1047
2	1025	910
3	3860	865
done	5000	861

prune545.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (sqrt (hypot re im)))
0.6b	(cbrt (sqrt (hypot re im)))
7.7b	(+ re (* (* (fabs (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (sqrt (hypot re im)))
2.0ms	(cbrt (sqrt (hypot re im)))
10.0ms	(+ re (* (* (fabs (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (hypot re im))
172.0ms	(cbrt (sqrt (hypot re im)))
159.0ms	(cbrt (sqrt (hypot re im)))
163.0ms	(+ re (* (* (fabs (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))))

simplify2.3s

Counts

73 → 73

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	109	1048
1	249	994
2	729	888
3	2508	867
done	5000	863

prune468.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.3b

regimes191.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample2.1s

Algorithm

intervals

Results

769.0ms	667×	body	2560	valid
571.0ms	6062×	body	80	valid
219.0ms	305×	body	5120	valid
148.0ms	490×	body	1280	valid
69.0ms	279×	body	640	valid
65.0ms	126×	body	320	valid
9.0ms	71×	body	160	valid