Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	198×	body	80	valid
6.0ms	21×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	10×	body	5120	valid
1.0ms	7×	body	640	valid
0.0ms	2×	body	320	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

prune4.0ms

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: 35.7b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
26.7b	(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)))

series138.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* re re) (* im im))
60.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (58.0ms)

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

prune289.0ms

Filtered

47 candidates to 38 candidates (19.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	41	6	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	6	48

Merged error: 15.4b

Counts

48 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.8b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

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:

18.0ms	(* (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)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
61.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
50.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

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

prune819.0ms

Filtered

136 candidates to 74 candidates (45.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Merged error: 15.4b

Counts

142 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (+ (* re re) (* im im))) re)
5.4b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
20.2b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
21×	`unpow-prod-down`
20×	`difference-of-squares`
14×	`sqrt-prod`
10×	`distribute-lft-out--`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
7×	`unpow2` `sqr-pow`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `sqrt-div` `div-exp`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 120

Calls

4 calls:

10.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (sqrt (+ (* re re) (* im im))) re)
292.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
96.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	440	1427
1	1601	1331
2	5002	1323

prune1.1s

Filtered

132 candidates to 84 candidates (36.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	129	9	138

Merged error: 13.2b

Counts

138 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (+ (* re re) (* im im))) re)
5.4b	(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
7×	`sqrt-div`
6×	`add-cube-cbrt` `add-log-exp`
5×	`sqrt-pow1`
4×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
3×	`pow1/2` `pow-prod-down`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `diff-log` `associate-*l/` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
22.0ms	(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (sqrt (+ (* re re) (* im im))) re)
297.0ms	(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
50.0ms	(sqrt (+ (* re re) (* im im)))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	287	589
1	1003	559
2	3783	555
3	5001	553

prune605.0ms

Filtered

72 candidates to 57 candidates (20.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	73	8	81

Merged error: 11.1b

Counts

81 → 8

regimes278.0ms

Accuracy

55.9% (11.5b remaining)

Error of 22.6b against oracle of 11.1b and baseline of 37.1b

bsearch85.0ms

Steps

Iters	Range		Point
5	2.2866843337900248e+77	5.514542683406611e+77	5.074607332841625e+77
6	-2.3668867758909003e-262	-3.904420795897775e-263	-3.969766570937923e-263

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample967.0ms

Algorithm

intervals

Results

279.0ms	6010×	body	80	valid
187.0ms	690×	body	2560	valid
112.0ms	507×	body	1280	valid
89.0ms	272×	body	5120	valid
60.0ms	300×	body	640	valid
21.0ms	145×	body	320	valid
7.0ms	76×	body	160	valid

Details

sample37.0ms

simplify5.0ms

prune4.0ms

localize15.0ms

rewrite16.0ms

series138.0ms

simplify63.0ms

prune289.0ms

localize12.0ms

rewrite45.0ms

series201.0ms

simplify49.0ms

prune819.0ms

localize13.0ms

rewrite42.0ms

series496.0ms

simplify56.0ms

prune1.1s

localize14.0ms

rewrite38.0ms

series460.0ms

simplify100.0ms

prune605.0ms

regimes278.0ms

bsearch85.0ms

simplify2.0ms

end0.0ms

sample967.0ms

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