Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample24.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

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: 31.9b

Counts

2 → 1

localize11.0ms

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))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

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))
11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series32.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
20.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	259	745
1	894	701
2	2872	696
3	5001	694

prune178.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 7.1b

Counts

84 → 13

localize15.0ms

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)))
30.6b	(log (+ (* re re) (* im im)))

rewrite50.0ms

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))))
8.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
34.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
12.0ms	(log (+ (* re re) (* im im)))

simplify191.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (172.0ms)

Iter	Nodes	Cost
0	563	2179
1	2462	2003
2	5002	1905

prune362.0ms

Filtered

106 candidates to 176 candidates (-66.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	178	11	189

Merged error: 6.9b

Counts

189 → 11

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))))))
13.0b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
18.6b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite32.0ms

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))
12.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
4.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
7.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
46.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
34.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
40.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	569	1798
1	2642	1588
2	5001	1456

prune347.0ms

Filtered

91 candidates to 140 candidates (-53.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Merged error: 6.9b

Counts

151 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
1.0b	(sqrt (sqrt (log 10.0)))
1.0b	(sqrt (sqrt (log 10.0)))
30.6b	(log (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
60×	`times-frac`
56×	`add-sqr-sqrt`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`cbrt-prod`
18×	`pow1`
10×	`associate-/r*` `log-pow`
8×	`sqrt-pow1`
7×	`add-exp-log`
6×	`associate-/l*`
5×	`add-cbrt-cube`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
3×	`log-prod`
2×	`log-div`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 142

Calls

4 calls:

9.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
2.0ms	(sqrt (sqrt (log 10.0)))
2.0ms	(sqrt (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series10.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
0.0ms	(sqrt (sqrt (log 10.0)))
0.0ms	(sqrt (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	279	1327
1	647	1276
2	1708	1194
3	5001	1182

prune476.0ms

Filtered

82 candidates to 148 candidates (-80.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	146	14	160

Merged error: 6.8b

Counts

160 → 14

regimes752.0ms

Accuracy

59.2% (9.8b remaining)

Error of 17.5b against oracle of 7.7b and baseline of 31.8b

bsearch67.0ms

Steps

Iters	Range		Point
9	9.870520066176808e+61	1.6884858656262616e+69	1.6682341796553902e+69
7	-3.4829089375383145e+136	-1.4656606149141445e+135	-7.386924077773248e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	43
1	51	43

end0.0ms

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample690.0ms

Algorithm

intervals

Results

540.0ms

8000×

body

valid

Details

analyze5.0ms

sample24.0ms

simplify3.0ms

prune3.0ms

localize11.0ms

rewrite21.0ms

series32.0ms

simplify91.0ms

prune178.0ms

localize15.0ms

rewrite50.0ms

series74.0ms

simplify191.0ms

prune362.0ms

localize20.0ms

rewrite32.0ms

series125.0ms

simplify69.0ms

prune347.0ms

localize22.0ms

rewrite22.0ms

series10.0ms

simplify55.0ms

prune476.0ms

regimes752.0ms

bsearch67.0ms

simplify2.0ms

end0.0ms

analyze4.0ms

sample690.0ms

Profiling