Details

sample25.0ms

Algorithm

intervals

Results

16.0ms

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 (0.0%)

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: 33.7b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

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:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* re re) (* im im))
144.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	256	741
1	895	697
2	2846	694
3	5001	694

prune216.0ms

Filtered

83 candidates to 55 candidates (66.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 8.3b

Counts

84 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
32.4b	(log (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
83×	`add-sqr-sqrt`
54×	`sqrt-prod`
53×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
19×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`div-sub`
1×	`+-commutative` `frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 164

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
25.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
154.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
206.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
54.0ms	(log (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	563	2159
1	2395	1981
2	5002	1899

prune387.0ms

Filtered

176 candidates to 104 candidates (59.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	9	176
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	178	12	190

Merged error: 8.1b

Counts

190 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
15.3b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
18.0b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`times-frac`
40×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
13×	`pow1`
12×	`add-exp-log` `unpow-prod-down`
9×	`add-cbrt-cube`
8×	`log-pow`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-log-exp`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-pow` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
14.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
5.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
8.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* re re) (* im im))
431.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
324.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
340.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	554	1776
1	2519	1567
2	5002	1445

prune353.0ms

Filtered

140 candidates to 89 candidates (63.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	138	14	152

Merged error: 8.1b

Counts

152 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
32.4b	(log (+ (* re re) (* im im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
112×	`times-frac`
107×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-l`
42×	`pow1`
33×	`associate-r`
31×	`log-pow`
21×	`add-exp-log`
20×	`add-cbrt-cube`
12×	`unswap-sqr`
10×	`sqrt-div`
7×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`frac-times` `associate-*r/`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `log-prod` `div-exp`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`frac-2neg` `rem-log-exp` `clear-num`

Counts

4 → 207

Calls

4 calls:

30.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
20.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series1.2s

Counts

4 → 12

Calls

4 calls:

645.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
245.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
210.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
51.0ms	(log (+ (* re re) (* im im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	640	3173
1	2753	2921
2	5002	2883

prune535.0ms

Filtered

219 candidates to 136 candidates (62.1%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	215	18	233

Merged error: 8.0b

Counts

233 → 18

regimes569.0ms

Accuracy

57.1% (10.5b remaining)

Error of 17.3b against oracle of 6.9b and baseline of 31.3b

bsearch218.0ms

Steps

Iters	Range		Point
9	9.092643328338922e+123	2.512579933221449e+133	7.579237005855668e+129
9	3.0514006174485665e-162	1.8222587195312444e-155	3.100418093247281e-162
9	9.929777800337937e-288	5.34670244842392e-280	4.7499823253112636e-281
9	-2.423146045177123e+82	-4.950444471151729e+75	-2.0900224301544303e+81

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	67
1	75	67

end0.0ms

sample662.0ms

Algorithm

intervals

Results

511.0ms

8000×

body

valid