Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	185×	body	80	valid
6.0ms	29×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	16×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8
done	46	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
17×	`sqrt-prod`
7×	`pow1`
6×	`fma-neg`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

3 → 74

Calls

3 calls:

54.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series258.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473
done	5001	473

prune186.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
0.4b	(- (* 1 (hypot re im)) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

0.0ms	(hypot re im)
20.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
9.0ms	(- (* 1 (hypot re im)) re)

series289.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(hypot re im)
181.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
58.0ms	(- (* 1 (hypot re im)) re)

simplify33.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	235	265
1	803	220
2	5002	213
done	5002	213

prune146.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re))))
0.4b	(* (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
0.4b	(- (* 1 (hypot re im)) re)
0.4b	(- (* 1 (hypot re im)) re)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
31×	`sqrt-prod`
28×	`add-sqr-sqrt` `sqrt-div`
23×	`pow-prod-down`
20×	`pow1/2`
17×	`*-un-lft-identity`
16×	`associate-*r/`
15×	`add-cube-cbrt`
14×	`pow-prod-up`
9×	`flip3--` `swap-sqr` `flip--`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `prod-diff` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `fma-neg` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

12.0ms	(sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re))))
97.0ms	(* (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
9.0ms	(- (* 1 (hypot re im)) re)
9.0ms	(- (* 1 (hypot re im)) re)

series540.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re))))
185.0ms	(* (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
58.0ms	(- (* 1 (hypot re im)) re)
61.0ms	(- (* 1 (hypot re im)) re)

simplify70.0ms

Counts

152 → 152

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	431	1161
1	1896	997
2	5001	968
done	5001	968

prune371.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
0.4b	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
0.4b	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
0.7b	(pow (cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re))))) 4)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
20×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div`
10×	`unpow-prod-down`
6×	`cbrt-div` `associate-*r/`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `flip3--` `flip--`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

13.0ms	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
13.0ms	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
16.0ms	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
11.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re))))) 4)

series1.4s

Counts

4 → 12

Calls

4 calls:

324.0ms	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
320.0ms	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
315.0ms	(cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re)))))
450.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (- (* 1 (hypot re im)) re))))) 4)

simplify45.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	372	1248
1	1186	1175
2	5001	1131
done	5001	1131

prune394.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.4b

regimes122.0ms

Accuracy

26.6% (4.4b remaining)

Error of 12.1b against oracle of 7.7b and baseline of 13.7b

bsearch72.0ms

Steps

Iters	Range		Point
10	6.203544841310545e+55	2.3069922374741435e+70	1.6666296725523275e+65

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	37	14
2	37	14
done	37	14

end0.0ms

sample749.0ms

Algorithm

intervals

Results

210.0ms	5947×	body	80	valid
143.0ms	726×	body	2560	valid
83.0ms	528×	body	1280	valid
72.0ms	294×	body	5120	valid
38.0ms	284×	body	640	valid
13.0ms	136×	body	320	valid
5.0ms	85×	body	160	valid