Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	196×	body	80	valid
7.0ms	27×	body	2560	valid
3.0ms	9×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	6×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

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 (100.0%)

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: 38.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune116.0ms

Filtered

63 candidates to 52 candidates (17.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	5	64

Merged error: 19.1b

Counts

64 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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)))))
14.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

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

prune131.0ms

Filtered

136 candidates to 75 candidates (44.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Merged error: 19.1b

Counts

141 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

4.8b	(exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
7.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

15.0ms	(exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
18.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify117.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (110.0ms)

Iter	Nodes	Cost
0	193	715
1	489	591
2	1180	550
3	3706	542
4	5002	540

prune132.0ms

Filtered

70 candidates to 60 candidates (14.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	69	8	77

Merged error: 19.1b

Counts

77 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(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)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify142.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (136.0ms)

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

prune134.0ms

Filtered

72 candidates to 60 candidates (16.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 19.1b

Counts

80 → 8

regimes258.0ms

Accuracy

57.1% (9.2b remaining)

Error of 26.8b against oracle of 17.6b and baseline of 39.2b

bsearch30.0ms

Steps

Iters	Range		Point
6	3.9313145927311245e+121	2.0989723635039152e+122	1.0048104163764278e+122
9	2.9048255267141237e-286	2.675646355851914e-280	2.945526040901568e-286

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample988.0ms

Algorithm

intervals

Results

295.0ms	6021×	body	80	valid
187.0ms	669×	body	2560	valid
119.0ms	527×	body	1280	valid
102.0ms	287×	body	5120	valid
48.0ms	271×	body	640	valid
18.0ms	136×	body	320	valid
10.0ms	89×	body	160	valid

Details

sample34.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series43.0ms

simplify95.0ms

prune116.0ms

localize12.0ms

rewrite42.0ms

series27.0ms

simplify49.0ms

prune131.0ms

localize16.0ms

rewrite43.0ms

series26.0ms

simplify117.0ms

prune132.0ms

localize30.0ms

rewrite18.0ms

series23.0ms

simplify142.0ms

prune134.0ms

regimes258.0ms

bsearch30.0ms

simplify2.0ms

end0.0ms

sample988.0ms

Profiling