Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
14.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* re re) (* im im))
148.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

83 → 83

Iterations

Useful iterations: 3 (413.0ms)

Iter	Nodes	Cost
0	125	1357
1	255	1281
2	738	1165
3	2843	1163
done	5001	1163

prune236.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt` `log-pow`
53×	`pow1`
46×	`associate-r`
28×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`flip3-+` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`+-commutative` `frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 205

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
45.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
12.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
149.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
221.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify889.0ms

Counts

217 → 217

Iterations

Useful iterations: 2 (275.0ms)

Iter	Nodes	Cost
0	247	4621
1	645	4164
2	1962	3647
done	5000	3647

prune453.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im)))))
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`cbrt-prod`
29×	`sqrt-prod`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`sqrt-div`
14×	`pow1`
12×	`cbrt-div`
11×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `flip-+` `unswap-sqr`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

27.0ms	(* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (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)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im)))))
42.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

121 → 121

Iterations

Useful iterations: 3 (544.0ms)

Iter	Nodes	Cost
0	113	2528
1	218	2267
2	664	2057
3	2705	1871
done	5001	1871

prune389.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))))
0.3b	(* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

156×	`sqrt-prod`
150×	`times-frac`
132×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
77×	`add-cube-cbrt`
64×	`log-pow`
61×	`pow1`
56×	`associate-l`
47×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
18×	`unswap-sqr`
16×	`sqrt-pow1` `pow1/2`
14×	`sqrt-div`
7×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`frac-times` `associate-r/` `associate-/l`
4×	`pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`log-div` `flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`rem-sqrt-square` `frac-2neg` `clear-num`

Counts

4 → 244

Calls

4 calls:

59.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))))
48.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
14.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series878.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))))
471.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
214.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify836.0ms

Counts

256 → 256

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	284	6214
1	661	5561
2	1815	5147
done	5001	4921

prune650.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.3b

regimes878.0ms

Accuracy

57.2% (10.7b remaining)

Error of 18.3b against oracle of 7.6b and baseline of 32.6b

bsearch172.0ms

Steps

Iters	Range		Point
8	1.5491720421655856e+95	6.147715137559524e+97	4.571695048514602e+96
8	6.003002310454003e-248	2.4211658919920166e-243	1.7146334702710424e-243
5	-4.555045930326338e-177	-1.9154334448410318e-177	-1.971567869430071e-177
9	-1.0311234165817051e+145	-1.4395777107888637e+138	-4.7575996220618e+138

simplify82.0ms

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	44	121
1	69	121
2	83	119
3	97	119
4	110	119
5	134	119
6	162	119
7	191	119
8	219	119
9	235	119
done	235	119

end0.0ms

sample495.0ms

Algorithm

intervals

Results

352.0ms

8000×

body

valid