Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

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: 30.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.7b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* re re) (* im im))
137.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (21.0ms)

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

prune209.0ms

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: 8.9b

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))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.7b	(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))
28.0ms	(* (/ 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)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* re re) (* im im))
143.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
199.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
48.0ms	(log (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (48.0ms)

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

prune394.0ms

Filtered

176 candidates to 104 candidates (59.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	166	10	176
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	176	14	190

Merged error: 8.8b

Counts

190 → 14

localize19.0ms

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))))))
12.3b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
17.5b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite34.0ms

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)))))
8.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
413.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
303.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
324.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify76.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (54.0ms)

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

prune359.0ms

Filtered

140 candidates to 89 candidates (63.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	138	16	154

Merged error: 8.8b

Counts

154 → 16

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (log (+ (* re re) (* im im))) (/ (/ 1/2 (sqrt (log 10.0))) (sqrt (log 10.0))))
28.7b	(log (+ (* re re) (* im im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

332×	`times-frac`
189×	`sqrt-prod`
179×	`associate-r`
178×	`add-sqr-sqrt`
154×	`add-cube-cbrt` `*-un-lft-identity`
53×	`pow1`
48×	`log-pow`
13×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`div-inv`
7×	`unswap-sqr`
5×	`add-log-exp`
4×	`associate-l`
3×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp` `cbrt-unprod`
2×	`log-div` `flip3-+` `flip-+`
1×	`+-commutative` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `-commutative`

Counts

3 → 231

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
55.0ms	(* (log (+ (* re re) (* im im))) (/ (/ 1/2 (sqrt (log 10.0))) (sqrt (log 10.0))))
4.0ms	(log (+ (* re re) (* im im)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* re re) (* im im))
151.0ms	(* (log (+ (* re re) (* im im))) (/ (/ 1/2 (sqrt (log 10.0))) (sqrt (log 10.0))))
50.0ms	(log (+ (* re re) (* im im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	886	2996
1	4365	2543
2	5002	2530

prune406.0ms

Filtered

240 candidates to 105 candidates (43.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	242	14	256

Merged error: 8.7b

Counts

256 → 14

regimes438.0ms

Accuracy

59.6% (10.0b remaining)

Error of 17.0b against oracle of 7.1b and baseline of 31.7b

bsearch79.0ms

Steps

Iters	Range		Point
7	5.385851842895965e+128	1.3149157288660681e+131	6.137182478245054e+128
7	-4.710268451496385e+120	-1.940140840912921e+118	-2.6754129982365756e+119

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	57	34
3	59	34
4	59	34

end0.0ms

sample491.0ms

Algorithm

intervals

Results

350.0ms

8000×

body

valid