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

sample28.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify3.0ms

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: 33.4b

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))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

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)))

series29.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4916	1166
1	4916	1166

prune173.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	67	16	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	16	84

Merged error: 8.3b

Counts

84 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
32.1b	(log (+ (* re re) (* im im)))

rewrite42.0ms

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))
21.0ms	(* (/ 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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
20.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
24.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4984	3029
1	4984	3029

prune309.0ms

Filtered

106 candidates to 176 candidates (-66.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	168	8	176
Fresh	12	3	15
Picked	1	0	1
Done	0	0	0
Total	181	11	192

Merged error: 8.2b

Counts

192 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
15.8b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
17.3b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite31.0ms

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))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
42.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
32.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
36.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4931	2232
1	4931	2232

prune273.0ms

Filtered

89 candidates to 140 candidates (-57.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	138	13	151

Merged error: 8.2b

Counts

151 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (sqrt (log 10.0)))
1.0b	(sqrt (sqrt (log 10.0)))
1.0b	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
32.1b	(log (+ (* re re) (* im im)))

rewrite19.0ms

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:

2.0ms	(sqrt (sqrt (log 10.0)))
2.0ms	(sqrt (sqrt (log 10.0)))
6.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
4.0ms	(log (+ (* re re) (* im im)))

series9.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt (sqrt (log 10.0)))
0.0ms	(sqrt (sqrt (log 10.0)))
0.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
9.0ms	(log (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5478	1608

prune398.0ms

Filtered

87 candidates to 148 candidates (-70.1%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	145	16	161

Merged error: 8.1b

Counts

161 → 16

regimes774.0ms

Accuracy

55.2% (10.7b remaining)

Error of 18.2b against oracle of 7.4b and baseline of 31.3b

bsearch58.0ms

Steps

Iters	Range		Point
3	6.979015859746455e+88	8.95741849777282e+88	8.833768332896172e+88
7	2.4257570276598574e-180	1.322199011196699e-178	2.4695374740654386e-180
7	-1.6564863711186631e-152	-1.0715581363280864e-154	-1.0928214580192916e-154
9	-5.1978392957765744e+107	-6.084853855880593e+99	-5.2032752033560465e+103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	115
1	64	115

end0.0ms

sample637.0ms

Algorithm

intervals

Results

496.0ms

8000×

body

valid

Details

analyze5.0ms

sample28.0ms

simplify3.0ms

prune3.0ms

localize11.0ms

rewrite16.0ms

series29.0ms

simplify50.0ms

prune173.0ms

localize15.0ms

rewrite42.0ms

series58.0ms

simplify73.0ms

prune309.0ms

localize19.0ms

rewrite31.0ms

series115.0ms

simplify49.0ms

prune273.0ms

localize21.0ms

rewrite19.0ms

series9.0ms

simplify61.0ms

prune398.0ms

regimes774.0ms

bsearch58.0ms

simplify2.0ms

end0.0ms

sample637.0ms

Profiling