Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	184×	body	80	valid
7.0ms	27×	body	2560	valid
6.0ms	15×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	14×	body	320	valid
1.0ms	7×	body	640	valid
0.0ms	1×	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 (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: 36.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

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

series82.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	141	198
1	358	186
2	866	182
3	2557	181
4	5001	181

prune105.0ms

Filtered

33 candidates to 29 candidates (87.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	5	34

Merged error: 16.4b

Counts

34 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

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:

15.0ms	(* (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)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
44.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(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

prune277.0ms

Filtered

136 candidates to 74 candidates (54.4%)

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: 16.4b

Counts

141 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

26.5b	(sqrt (+ (* re re) (* im im)))
27.4b	(cbrt (+ (* re re) (* im im)))
27.4b	(cbrt (+ (* re re) (* im im)))
27.4b	(cbrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

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

series314.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))
99.0ms	(cbrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	141	466
1	440	436
2	1469	430
3	5002	429

prune344.0ms

Filtered

66 candidates to 60 candidates (90.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	66	7	73

Merged error: 16.4b

Counts

73 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
33.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(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

prune302.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 16.4b

Counts

79 → 7

regimes195.0ms

Accuracy

54.8% (9.6b remaining)

Error of 27.8b against oracle of 18.2b and baseline of 39.4b

bsearch100.0ms

Steps

Iters	Range	Point
9	4.0160950957056723e+121	1.2392158031794936e+127	4.493210959094433e+125
2	1.834686345066682e-161	2.1192662046019758e-161	1.8702588275085934e-161
9	2.852999908040723e-205	7.330065439830617e-197	7.184067081095878e-197

Iters

Range

Point

4.0160950957056723e+121

1.2392158031794936e+127

4.493210959094433e+125

1.834686345066682e-161

2.1192662046019758e-161

1.8702588275085934e-161

2.852999908040723e-205

7.330065439830617e-197

7.184067081095878e-197

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	33
1	43	33

end0.0ms

sample907.0ms

Algorithm

intervals

Results

285.0ms	6005×	body	80	valid
197.0ms	700×	body	2560	valid
114.0ms	497×	body	1280	valid
93.0ms	267×	body	5120	valid
50.0ms	283×	body	640	valid
20.0ms	149×	body	320	valid
9.0ms	99×	body	160	valid