Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.4b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

24.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
16.0ms	(sqrt (+ (* re re) (* im im)))

series179.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify132.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 4 (124.0ms)

Iter	Nodes	Cost
0	218	683
1	563	650
2	1335	648
3	4557	648
4	5001	647

prune173.0ms

Filtered

74 candidates to 45 candidates (39.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	58	16	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	16	75

Merged error: 8.9b

Counts

75 → 16

localize13.0ms

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)))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

224×	`associate-/r*`
208×	`frac-times`
207×	`sqrt-prod`
200×	`add-sqr-sqrt`
172×	`*-un-lft-identity`
153×	`add-cube-cbrt`
143×	`associate-/l*`
135×	`log-pow`
127×	`times-frac`
112×	`pow1`
46×	`associate-r`
33×	`clear-num`
32×	`frac-2neg`
30×	`sqrt-pow1` `pow1/2`
29×	`associate-l`
27×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-*r/`
15×	`unswap-sqr`
13×	`associate-*l/`
9×	`div-exp`
8×	`prod-exp`
5×	`cbrt-undiv` `distribute-lft-out`
4×	`sqrt-div` `cbrt-unprod`
3×	`un-div-inv` `div-inv` `add-log-exp`
2×	`log-div` `rec-exp` `flip3-+` `1-exp` `div-sub` `swap-sqr` `flip-+`
1×	`rem-sqrt-square` `pow-prod-down` `*-commutative`

Counts

3 → 436

Calls

3 calls:

40.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
24.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series395.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(* (/ 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)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify146.0ms

Algorithm

egg-herbie

Counts

445 → 445

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1217	5699
1	4602	5227
2	5001	5045

prune468.0ms

Filtered

445 candidates to 140 candidates (68.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	431	14	445
Fresh	11	4	15
Picked	1	0	1
Done	0	0	0
Total	443	18	461

Merged error: 8.8b

Counts

461 → 18

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
0.3b	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

277×	`add-sqr-sqrt`
224×	`associate-/r*`
211×	`associate-*r/`
208×	`frac-times`
198×	`*-un-lft-identity` `sqrt-prod`
145×	`add-cube-cbrt`
115×	`times-frac`
111×	`associate-/l*`
91×	`associate-r`
77×	`add-exp-log`
65×	`unswap-sqr`
56×	`pow1`
47×	`clear-num` `log-pow`
45×	`un-div-inv`
41×	`associate-l`
40×	`prod-exp`
32×	`frac-2neg`
29×	`add-cbrt-cube`
20×	`div-exp`
13×	`associate-*l/`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
6×	`cbrt-undiv`
5×	`distribute-lft-out`
4×	`pow-prod-down`
3×	`sqrt-pow1` `pow1/2` `*-commutative` `div-inv` `add-log-exp`
2×	`sqrt-div` `swap-sqr`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

3 → 456

Calls

3 calls:

15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
50.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
16.0ms	(sqrt (+ (* re re) (* im im)))

series399.0ms

Counts

3 → 9

Calls

3 calls:

211.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
144.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify144.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1152	6048
1	3964	5346
2	5001	4917

prune421.0ms

Filtered

465 candidates to 126 candidates (72.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	4	13	17
Picked	0	1	1
Done	0	0	0
Total	465	18	483

Merged error: 8.8b

Counts

483 → 18

localize15.0ms

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)
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
58×	`log-pow`
56×	`unpow-prod-down`
54×	`*-un-lft-identity`
51×	`pow1`
42×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
33×	`cbrt-prod`
14×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-prod`
6×	`associate-/l*`
5×	`distribute-lft-out`
4×	`pow-unpow` `sqrt-div` `associate-l` `associate-/r*` `add-log-exp`
3×	`div-inv`
2×	`cbrt-undiv` `log-div` `flip3-+` `unpow3` `div-sub` `swap-sqr` `div-exp` `pow-exp` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `pow1/3` `clear-num`

Counts

4 → 157

Calls

4 calls:

6.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
22.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
18.0ms	(sqrt (+ (* re re) (* im im)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
139.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
241.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	479	1786
1	1703	1740
2	5002	1720

prune298.0ms

Filtered

169 candidates to 97 candidates (42.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	161	8	169
Fresh	4	12	16
Picked	1	0	1
Done	0	1	1
Total	166	21	187

Merged error: 8.8b

Counts

187 → 21

regimes1.0s

Accuracy

57% (10.4b remaining)

Error of 17.8b against oracle of 7.4b and baseline of 31.6b

bsearch88.0ms

Steps

Iters	Range		Point
9	9.053381057383739e+60	1.5221618338087932e+67	5.770464360252651e+64
8	-1.1770646658396024e+45	-1.622771936437238e+42	-1.1374036108499898e+45

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	33
1	52	33
2	55	33
3	57	33
4	57	33

end0.0ms

sample500.0ms

Algorithm

intervals

Results

360.0ms

8000×

body

valid