Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
5.0ms	15×	body	1280	valid
4.0ms	19×	body	2560	valid
3.0ms	14×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

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: 37.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt`
3×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

3 → 38

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	178	275
1	689	252
2	2017	248
3	5001	246

prune136.0ms

Filtered

47 candidates to 38 candidates (80.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	7	48

Merged error: 18.9b

Counts

48 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.1b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
46.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
43.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune286.0ms

Filtered

136 candidates to 72 candidates (52.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 18.9b

Counts

143 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify141.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (134.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune311.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 18.9b

Counts

80 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
13.6b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
17.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
46.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	394	992
1	1342	878
2	5001	845

prune291.0ms

Filtered

103 candidates to 65 candidates (63.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	103	8	111

Merged error: 18.9b

Counts

111 → 8

regimes195.0ms

Accuracy

57.5% (9.0b remaining)

Error of 26.7b against oracle of 17.7b and baseline of 38.9b

bsearch90.0ms

Steps

Iters	Range		Point
7	5.385851842895965e+128	1.3149157288660681e+131	9.636008637468581e+128
9	2.421478779902882e-177	9.2681278916812e-172	2.457269547281343e-177

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	58
1	43	58

end0.0ms

sample686.0ms

Algorithm

intervals

Results

201.0ms	6028×	body	80	valid
134.0ms	692×	body	2560	valid
85.0ms	497×	body	1280	valid
64.0ms	264×	body	5120	valid
39.0ms	286×	body	640	valid
20.0ms	160×	body	320	valid
7.0ms	73×	body	160	valid