Details

sample67.0ms

Algorithm

intervals

Results

15.0ms	185×	body	80	valid
14.0ms	30×	body	2560	valid
7.0ms	18×	body	1280	valid
5.0ms	8×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.3b	(+ 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))
12.0ms	(+ re (hypot re im))

series414.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(hypot re im)
261.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
91.0ms	(+ re (hypot re im))

simplify2.4s

Counts

51 → 51

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	617	354
3	3785	345
done	5000	344

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.9b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`associate-*l/`
18×	`cbrt-div` `sqrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
7×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

54.0ms	(* (cbrt (sqrt (* (+ re (hypot re im)) 2.0))) (cbrt (sqrt (* (+ re (hypot re im)) 2.0))))
8.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))
12.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))
16.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))

series2.0s

Counts

4 → 12

Calls

4 calls:

606.0ms	(* (cbrt (sqrt (* (+ re (hypot re im)) 2.0))) (cbrt (sqrt (* (+ re (hypot re im)) 2.0))))
500.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))
456.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))
456.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))

simplify904.0ms

Counts

113 → 113

Iterations

Useful iterations: done (899.0ms)

Iter	Nodes	Cost
0	169	2431
1	371	2241
2	1278	2090
done	5001	1935

prune938.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*l/`
16×	`cbrt-div`
13×	`add-sqr-sqrt`
11×	`cbrt-prod` `*-un-lft-identity`
9×	`add-cube-cbrt` `flip3-+` `flip-+`
8×	`sqrt-div`
7×	`associate-r`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `pow1/3` `associate-l` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-*r/` `pow-prod-down` `sqrt-prod` `unswap-sqr`
1×	`+-commutative` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

6.0ms	(+ re (hypot re im))
36.0ms	(* (cbrt (* (+ re (hypot re im)) 2.0)) (cbrt (sqrt (* (+ re (hypot re im)) 2.0))))
13.0ms	(cbrt (* (+ re (hypot re im)) 2.0))
9.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ re (hypot re im))
797.0ms	(* (cbrt (* (+ re (hypot re im)) 2.0)) (cbrt (sqrt (* (+ re (hypot re im)) 2.0))))
270.0ms	(cbrt (* (+ re (hypot re im)) 2.0))
494.0ms	(cbrt (sqrt (* (+ re (hypot re im)) 2.0)))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	203	1663
1	467	1596
2	1602	1506
done	5000	1472

prune661.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.9b

localize28.0ms

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)))
7.1b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite32.0ms

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))
8.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
14.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series559.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (hypot re im))
268.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
79.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
71.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify1.2s

Counts

109 → 109

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	143	1359
1	337	767
2	1439	698
done	5001	689

prune512.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.8b

regimes187.0ms

Accuracy

0% (2.1b remaining)

Error of 15.1b against oracle of 13.1b and baseline of 15.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	23
1	20	23
done	20	23

end0.0ms

sample2.1s

Algorithm

intervals

Results

680.0ms	6022×	body	80	valid
545.0ms	472×	body	1280	valid
272.0ms	671×	body	2560	valid
167.0ms	308×	body	5120	valid
79.0ms	300×	body	640	valid
29.0ms	149×	body	320	valid
10.0ms	78×	body	160	valid