Details

analyze9.0ms

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

sample40.0ms

Algorithm

intervals

Results

27.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

prune6.0ms

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: 30.8b

Counts

2 → 1

localize12.0ms

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))
28.6b	(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))
8.0ms	(/ (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))
21.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4916	1166
1	4916	1166

prune167.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

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: 7.2b

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)))
29.6b	(log (+ (* re re) (* im im)))

rewrite44.0ms

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))
22.0ms	(* (/ 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))))
21.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
11.0ms	(log (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4984	3029
1	4984	3029

prune315.0ms

Filtered

106 candidates to 176 candidates (-66.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	8	176
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	178	12	190

Merged error: 7.1b

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))))))
12.2b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
18.7b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite33.0ms

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))
13.0ms	(* (/ 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)))))
7.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
44.0ms	(* (/ 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)))))
37.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4931	2232
1	4931	2232

prune309.0ms

Filtered

88 candidates to 140 candidates (-59.1%)

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: 7.1b

Counts

152 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
0.4b	(* (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)))
29.6b	(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:

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

series104.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
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))))))
21.0ms	(/ (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 (45.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune483.0ms

Filtered

135 candidates to 219 candidates (-62.2%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	212	7	219
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	215	18	233

Merged error: 7.0b

Counts

233 → 18

regimes1.3s

Accuracy

51.9% (11.8b remaining)

Error of 19.1b against oracle of 7.3b and baseline of 31.8b

bsearch75.0ms

Steps

Iters	Range		Point
7	7.831892764795987e+115	2.2347930020516553e+117	2.3077438582071508e+116
9	-6.3022215523443915e-276	-4.703267648236281e-283	-6.218827239863813e-276
9	-3.831304273694772e-200	-4.8483976847697235e-208	-4.948094964353528e-208
8	-315939695.75913996	-5463.051143064723	-307633288.5871727

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	117
1	55	117

end0.0ms

sample619.0ms

Algorithm

intervals

Results

486.0ms

8000×

body

valid

Details

analyze9.0ms

sample40.0ms

simplify4.0ms

prune6.0ms

localize12.0ms

rewrite18.0ms

series32.0ms

simplify51.0ms

prune167.0ms

localize13.0ms

rewrite44.0ms

series58.0ms

simplify77.0ms

prune315.0ms

localize20.0ms

rewrite33.0ms

series118.0ms

simplify49.0ms

prune309.0ms

localize15.0ms

rewrite64.0ms

series104.0ms

simplify70.0ms

prune483.0ms

regimes1.3s

bsearch75.0ms

simplify2.0ms

end0.0ms

sample619.0ms

Profiling