Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	186×	body	80	valid
9.0ms	18×	body	1280	valid
9.0ms	24×	body	2560	valid
5.0ms	12×	body	5120	valid
2.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify33.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.0b	(hypot re im)
0.4b	(+ re (hypot re im))

rewrite31.0ms

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:

17.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
1.0ms	(hypot re im)
12.0ms	(+ re (hypot re im))

series443.0ms

Counts

3 → 9

Calls

3 calls:

255.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
83.0ms	(hypot re im)
105.0ms	(+ re (hypot re im))

simplify4.6s

Counts

51 → 51

Iterations

Useful iterations: 4 (2.2s)

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

prune225.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.0b	(hypot re im)
0.3b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
0.4b	(+ re (hypot re im))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`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×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 81

Calls

4 calls:

12.0ms	(sqrt (+ re (hypot re im)))
0.0ms	(hypot re im)
27.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
10.0ms	(+ re (hypot re im))

series537.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(sqrt (+ re (hypot re im)))
53.0ms	(hypot re im)
209.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
103.0ms	(+ re (hypot re im))

simplify4.2s

Counts

93 → 93

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	135	898
1	298	819
2	742	778
3	1970	766
done	5000	764

prune321.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.8b

localize14.0ms

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)))
11.1b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite40.0ms

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)
7.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
18.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
12.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot re im)
281.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
71.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
89.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify2.8s

Counts

104 → 104

Iterations

Useful iterations: done (2.7s)

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

prune413.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 13.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.9b	(pow (sqrt (cbrt (hypot re im))) 4)
10.1b	(+ re (* (sqrt (hypot re im)) (sqrt (* (pow (sqrt (cbrt (hypot re im))) 4) (cbrt (hypot re im))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
5.0ms	(pow (sqrt (cbrt (hypot re im))) 4)
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (* (pow (sqrt (cbrt (hypot re im))) 4) (cbrt (hypot re im))))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (hypot re im))
176.0ms	(cbrt (hypot re im))
163.0ms	(pow (sqrt (cbrt (hypot re im))) 4)
95.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (* (pow (sqrt (cbrt (hypot re im))) 4) (cbrt (hypot re im))))))

simplify1.8s

Counts

83 → 83

Iterations

Useful iterations: 3 (616.0ms)

Iter	Nodes	Cost
0	122	1013
1	270	938
2	635	702
3	1450	550
done	5000	550

prune441.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.8b

regimes140.0ms

Accuracy

0% (0.6b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
done	13	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

298.0ms	6001×	body	80	valid
205.0ms	706×	body	2560	valid
122.0ms	510×	body	1280	valid
103.0ms	295×	body	5120	valid
47.0ms	261×	body	640	valid
21.0ms	153×	body	320	valid
7.0ms	74×	body	160	valid