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

sample23.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

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: 35.4b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

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:

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

series29.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5218	1035

prune151.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	55	14	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	14	70

Merged error: 10.3b

Counts

70 → 14

localize13.0ms

Local error

Found 3 expressions with local error:

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)))
34.0b	(log (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 153

Calls

3 calls:

22.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
9.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series54.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* (/ 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)))
9.0ms	(log (+ (* re re) (* im im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4936	2822
1	4936	2822

prune299.0ms

Filtered

96 candidates to 162 candidates (-68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	153	9	162
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	163	13	176

Merged error: 10.1b

Counts

176 → 13

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
34.0b	(log (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
46×	`times-frac`
45×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
29×	`associate-l` `add-cbrt-cube`
26×	`associate-r` `sqrt-prod`
22×	`prod-exp`
18×	`pow1`
12×	`cbrt-unprod`
11×	`div-exp`
8×	`log-pow`
6×	`cbrt-undiv`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`rec-exp` `log-prod` `1-exp` `un-div-inv` `add-log-exp`
2×	`frac-times` `log-div` `*-commutative` `div-inv`
1×	`flip3-+` `rem-log-exp` `associate-*l/` `flip-+`

Counts

3 → 122

Calls

3 calls:

13.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
11.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(log (+ (* re re) (* im im)))

series53.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
23.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
10.0ms	(log (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5202	1839

prune224.0ms

Filtered

74 candidates to 131 candidates (-77.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	131	13	144

Merged error: 10.1b

Counts

144 → 13

localize15.0ms

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))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
0.4b	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
34.0b	(log (+ (* re re) (* im im)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
112×	`times-frac`
107×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `*-un-lft-identity`
60×	`associate-l`
42×	`pow1`
31×	`log-pow`
29×	`associate-r`
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:

18.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
26.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
48.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune508.0ms

Filtered

135 candidates to 219 candidates (-62.2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	210	9	219
Fresh	5	6	11
Picked	0	1	1
Done	0	1	1
Total	215	17	232

Merged error: 10.1b

Counts

232 → 17

regimes1.2s

Accuracy

55.8% (10.6b remaining)

Error of 18.3b against oracle of 7.8b and baseline of 31.7b

bsearch79.0ms

Steps

Iters	Range		Point
7	6.783517405756766e+129	4.700326212607798e+131	5.756838278404119e+130
8	8.607226238382809e-199	3.519090005170553e-196	2.046877101973681e-198
9	-1.2081075676429345e-257	-1.2687005067456096e-262	-4.17385497808198e-261
10	-1.2829024005784942e+32	-6.624285637051713e+20	-1.268063321609487e+32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	128
1	75	128

end0.0ms

sample619.0ms

Algorithm

intervals

Results

483.0ms

8000×

body

valid

Details

analyze5.0ms

sample23.0ms

simplify2.0ms

prune3.0ms

localize10.0ms

rewrite13.0ms

series29.0ms

simplify83.0ms

prune151.0ms

localize13.0ms

rewrite40.0ms

series54.0ms

simplify81.0ms

prune299.0ms

localize14.0ms

rewrite35.0ms

series53.0ms

simplify53.0ms

prune224.0ms

localize15.0ms

rewrite64.0ms

series107.0ms

simplify70.0ms

prune508.0ms

regimes1.2s

bsearch79.0ms

simplify2.0ms

end0.0ms

sample619.0ms

Profiling