Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	194×	body	80	valid
3.0ms	15×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	29	10
3	31	10
done	31	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.7b	(+ re (hypot re im))

rewrite8.0ms

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:

0.0ms	(hypot re im)
4.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
3.0ms	(+ re (hypot re im))

series295.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(hypot re im)
191.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
59.0ms	(+ re (hypot re im))

simplify3.2s

Counts

51 → 51

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	460	354
3	1308	345
4	3946	344
done	5000	344

prune156.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize10.0ms

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))
0.6b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.3b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite15.0ms

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:

1.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
7.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
2.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (hypot re im))
189.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
45.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
61.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify1.5s

Counts

109 → 109

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	143	1359
1	310	757
2	839	698
3	2772	669
done	5001	668

prune264.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.6b	(* (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
10.2b	(+ re (* (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

87×	`sqrt-pow1`
81×	`sqrt-prod`
67×	`pow1`
57×	`add-sqr-sqrt`
45×	`pow1/2`
39×	`pow-prod-up`
21×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr`
15×	`associate-l`
12×	`pow-prod-down`
11×	`add-exp-log` `pow-sqr` `add-cbrt-cube` `unswap-sqr`
10×	`associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `rem-square-sqrt` `flip-+`

Counts

4 → 162

Calls

4 calls:

1.0ms	(sqrt (sqrt (hypot re im)))
12.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
30.0ms	(* (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
3.0ms	(+ re (* (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(sqrt (sqrt (hypot re im)))
87.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
44.0ms	(* (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
62.0ms	(+ re (* (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))))

simplify2.2s

Counts

174 → 174

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	179	2591
1	396	1121
2	989	1013
3	3561	975
done	5000	973

prune329.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(* (sqrt (hypot re im)) (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im))))))
9.4b	(+ re (* (sqrt (hypot re im)) (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-pow1`
28×	`pow-prod-up`
26×	`pow1/3`
25×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
12×	`pow1/2` `pow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `pow-sqr` `log1p-expm1-u`
3×	`fma-def` `sqrt-unprod` `sqrt-prod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 79

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
124.0ms	(* (sqrt (hypot re im)) (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im))))))
3.0ms	(+ re (* (sqrt (hypot re im)) (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (hypot re im))
106.0ms	(cbrt (hypot re im))
48.0ms	(* (sqrt (hypot re im)) (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im))))))
55.0ms	(+ re (* (sqrt (hypot re im)) (* (sqrt (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))) (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))))

simplify1.0s

Counts

91 → 91

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	141	2136
1	355	1547
2	1097	1243
done	5000	1238

prune401.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.8b

regimes137.0ms

Accuracy

0% (1.8b remaining)

Error of 14.8b against oracle of 13.0b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	17	23
done	17	23

end0.0ms

sample679.0ms

Algorithm

intervals

Results

211.0ms	6037×	body	80	valid
133.0ms	686×	body	2560	valid
84.0ms	520×	body	1280	valid
69.0ms	289×	body	5120	valid
34.0ms	277×	body	640	valid
11.0ms	121×	body	320	valid
5.0ms	70×	body	160	valid