Details

sample186.0ms

Algorithm

intervals

Results

78.0ms	198×	body	80	valid
9.0ms	21×	body	2560	valid
5.0ms	16×	body	1280	valid
3.0ms	6×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	17	15
2	24	15
3	30	15
4	35	15
done	35	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div`
3×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 43

Calls

3 calls:

34.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(- (sqrt (+ (* re re) (* im im))) re)
31.0ms	(sqrt (+ (* re re) (* im im)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

227.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
54.0ms	(- (sqrt (+ (* re re) (* im im))) re)
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.3s

Counts

52 → 52

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	106	776
1	230	671
2	603	621
3	1694	596
4	4451	590
done	5000	590

prune298.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize32.0ms

Local error

Found 4 expressions with local error:

9.7b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

168.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))
19.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
68.0ms	(sqrt (+ (* re re) (* im im)))
62.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

69 → 69

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	64	1227
1	150	1131
2	366	665
3	1069	626
4	3842	618
done	5000	616

prune452.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (* 2.0 (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
11×	`pow1`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `associate-/l*`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 93

Calls

4 calls:

78.0ms	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
64.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (* 2.0 (* im im)))
17.0ms	(sqrt (+ (* re re) (* im im)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
80.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
66.0ms	(sqrt (* 2.0 (* im im)))
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

105 → 105

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	181	2231
1	387	1998
2	1067	1907
3	3181	1877
done	5000	1871

prune498.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im))
0.3b	(/ (sqrt 2.0) (/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

318×	`times-frac`
223×	`*-un-lft-identity`
181×	`sqrt-prod`
172×	`add-sqr-sqrt`
171×	`add-cube-cbrt`
28×	`associate-/r*`
26×	`distribute-lft-out`
13×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `div-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/`

Counts

4 → 268

Calls

4 calls:

73.0ms	(/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im))
79.0ms	(/ (sqrt 2.0) (/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im)))
56.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im))
233.0ms	(/ (sqrt 2.0) (/ (sqrt (+ (sqrt (+ (* re re) (* im im))) re)) (fabs im)))
66.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
64.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

280 → 280

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	375	8428
1	842	7587
2	2490	7378
done	5000	7347

prune913.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.6b

regimes450.0ms

Accuracy

66.5% (10.0b remaining)

Error of 17.8b against oracle of 7.8b and baseline of 37.7b

bsearch227.0ms

Steps

Iters	Range		Point
8	3.643406663388999e+111	1.5037952905502068e+114	8.545763741641592e+113
8	-8.88757827843957e-288	-5.138571342544288e-291	-2.4372997740340113e-288
9	-8.553073611070034e-194	-1.0428205539953484e-198	-4.3557009877399066e-198
8	-7.0065691084106e+119	-2.7815652200329975e+115	-4.8976839775957715e+115

simplify15.0ms

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	51	103
1	64	102
done	64	102

end0.0ms

sample1.2s

Algorithm

intervals

Results

326.0ms	6037×	body	80	valid
232.0ms	712×	body	2560	valid
127.0ms	305×	body	5120	valid
124.0ms	462×	body	1280	valid
55.0ms	270×	body	640	valid
19.0ms	131×	body	320	valid
9.0ms	83×	body	160	valid