Details

sample137.0ms

Algorithm

intervals

Results

16.0ms	180×	body	80	valid
11.0ms	23×	body	2560	valid
7.0ms	12×	body	5120	valid
7.0ms	18×	body	1280	valid
4.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify107.0ms

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: 41.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite141.0ms

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:

39.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
88.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))

series371.0ms

Counts

3 → 9

Calls

3 calls:

232.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
57.0ms	(- (sqrt (+ (* re re) (* im im))) re)
81.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.4s

Counts

52 → 52

Iterations

Useful iterations: 4 (2.3s)

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

prune308.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize17.0ms

Local error

Found 4 expressions with local error:

12.5b	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite227.0ms

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:

189.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))
14.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
55.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
62.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.5s

Counts

69 → 69

Iterations

Useful iterations: done (3.5s)

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

prune354.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
30.1b	(sqrt (* 2.0 (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite167.0ms

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:

82.0ms	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
60.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
68.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
74.0ms	(sqrt (* 2.0 (* im im)))
68.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts

105 → 105

Iterations

Useful iterations: done (3.0s)

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

prune522.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
39×	`sqrt-prod`
37×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 125

Calls

4 calls:

85.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
170.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
37.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
272.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
87.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

137 → 137

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	248	2920
1	598	2628
2	2009	2460
done	5000	2407

prune646.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

regimes329.0ms

Accuracy

52.9% (13.9b remaining)

Error of 21.9b against oracle of 8.0b and baseline of 37.5b

bsearch243.0ms

Steps

Iters	Range		Point
7	3.0460639706602055e+56	5.294198543636e+57	5.2435161230838395e+57
9	1.0202828991379585e-254	1.1317114056863307e-247	3.824319967948722e-251
8	-8.084874607089052e-106	-1.5581536962061262e-110	-1.9984737931797426e-109
8	-1.3992557705202746e-39	-4.67729697810516e-44	-9.95874112743587e-42

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	96
1	64	96
done	64	96

end0.0ms

sample2.3s

Algorithm

intervals

Results

631.0ms	6068×	body	80	valid
628.0ms	269×	body	5120	valid
323.0ms	727×	body	2560	valid
213.0ms	450×	body	1280	valid
62.0ms	81×	body	160	valid
61.0ms	238×	body	640	valid
33.0ms	167×	body	320	valid