Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
3.0ms	17×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	23	15
done	23	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
183.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

63 → 63

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	108	888
1	272	774
2	845	698
3	2784	673
done	5001	672

prune192.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
7×	`pow1`
4×	`add-exp-log` `cbrt-prod` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div` `associate-*r/`
1×	`pow1/3`

Counts

4 → 59

Calls

4 calls:

11.0ms	(cbrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
4.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(cbrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
36.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify943.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (304.0ms)

Iter	Nodes	Cost
0	118	1065
1	267	925
2	719	866
3	2208	845
done	5001	845

prune300.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.6b

localize23.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	207	680
3	459	656
4	1009	656
5	2577	656
done	5000	656

prune355.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.1b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
3×	`log-pow`
2×	`+-commutative` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `sum-log`
1×	`rem-sqrt-square` `rem-exp-log` `distribute-lft-out`

Counts

4 → 60

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
23.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
39.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
47.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (307.0ms)

Iter	Nodes	Cost
0	108	993
1	222	795
2	619	707
3	2015	699
done	5001	699

prune189.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.5b

regimes382.0ms

Accuracy

56.1% (9.6b remaining)

Error of 26.4b against oracle of 16.8b and baseline of 38.6b

bsearch78.0ms

Steps

Iters	Range		Point
7	1.8684288122828866e+141	1.487546070235645e+143	6.674516804324248e+142
9	-1.6545147340030671e-295	-6.515465488001152e-301	-6.580886374598778e-301

simplify3.0ms

Iterations

Useful iterations: done (3.0ms)

Iter	Nodes	Cost
0	31	52
1	41	52
done	41	50

end0.0ms

sample686.0ms

Algorithm

intervals

Results

206.0ms	5999×	body	80	valid
130.0ms	657×	body	2560	valid
82.0ms	524×	body	1280	valid
71.0ms	295×	body	5120	valid
38.0ms	308×	body	640	valid
13.0ms	142×	body	320	valid
5.0ms	75×	body	160	valid