Details

sample56.0ms

Algorithm

intervals

Results

32.0ms

256×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

52.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
9.0ms	(sqrt (+ (* re re) (* im im)))

series306.0ms

Counts

2 → 6

Calls

2 calls:

255.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

69 → 69

Iterations

Useful iterations: 3 (442.0ms)

Iter	Nodes	Cost
0	116	1191
1	227	1120
2	559	1048
3	1892	1032
done	5001	1032

prune422.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize51.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 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)))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 194

Calls

3 calls:

74.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
47.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series540.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
282.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

203 → 203

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	238	4455
1	663	4119
2	3449	3702
done	5000	3528

prune947.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (sqrt (log 10.0)))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
28.3b	(sqrt (+ (* re re) (* im im)))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

290×	`sqrt-pow1`
247×	`pow1`
202×	`log-pow`
176×	`sqrt-prod`
175×	`times-frac`
146×	`pow1/2`
110×	`add-sqr-sqrt`
81×	`pow-prod-up`
78×	`add-cube-cbrt` `*-un-lft-identity`
52×	`sqrt-div`
45×	`pow-prod-down` `pow-sqr`
25×	`associate-/l*`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
9×	`pow2` `pow-plus` `associate-r` `associate-l` `unswap-sqr`
8×	`add-exp-log` `frac-times` `log-div` `div-sub` `add-cbrt-cube`
7×	`associate-/r*`
4×	`associate-r/` `associate-l/` `add-log-exp`
2×	`rem-sqrt-square`
1×	`cbrt-undiv` `frac-2neg` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 340

Calls

4 calls:

219.0ms	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (sqrt (log 10.0)))
77.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ (log (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))) (sqrt (log 10.0)))
44.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
63.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

352 → 352

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	339	9238
1	684	6231
2	2007	5805
done	5000	5782

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
0.7b	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
94×	`log-pow`
79×	`pow1`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
62×	`cbrt-prod`
56×	`unpow-prod-down` `cube-prod`
22×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv`
4×	`sqrt-div` `associate-/r*` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cbrt-undiv` `cube-div` `cube-mult` `log-div` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

4 → 211

Calls

4 calls:

14.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
36.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
14.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
17.0ms	(sqrt (+ (* re re) (* im im)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
197.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
306.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

223 → 223

Iterations

Useful iterations: 2 (647.0ms)

Iter	Nodes	Cost
0	218	5082
1	709	4353
2	3626	4033
done	5001	4033

prune668.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 5.2b

regimes2.2s

Accuracy

57.5% (10.4b remaining)

Error of 17.7b against oracle of 7.3b and baseline of 31.7b

bsearch111.0ms

Steps

Iters	Range		Point
8	1.8623232569795505e+82	7.764823604878808e+84	5.435137585363575e+84
5	-2.822584078228535e+117	-1.0610906721978556e+117	-2.4740957117892876e+117

simplify11.0ms

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	33	69
1	47	69
2	53	69
3	56	68
done	56	68

end0.0ms

sample1.2s

Algorithm

intervals

Results

919.0ms

8000×

body

valid