Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
8.0ms	20×	body	1280	valid
6.0ms	23×	body	2560	valid
2.0ms	7×	body	5120	valid
1.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

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

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: 38.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

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)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

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)))

simplify71.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	247	351
1	781	333
2	2656	327
3	5001	325

prune97.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 17.6b

Counts

50 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.6b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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)))))
16.0ms	(+ (* (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)))

series25.0ms

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

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

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

prune129.0ms

Filtered

74 candidates to 136 candidates (-83.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Merged error: 17.6b

Counts

142 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.6b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
17.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (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:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 4 (100.0ms)

Iter	Nodes	Cost
0	208	622
1	485	555
2	1193	507
3	3624	495
4	5003	493

prune124.0ms

Filtered

63 candidates to 75 candidates (-19.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	75	6	81

Merged error: 17.6b

Counts

81 → 6

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

6.0ms

(sqrt (* 2.0 (+ im re)))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(sqrt (* 2.0 (+ im re)))

simplify62.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	167	96
1	561	94
2	2387	92
3	5001	92

prune25.0ms

Filtered

14 candidates to 16 candidates (-14.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	16	6	22

Merged error: 17.6b

Counts

22 → 6

regimes228.0ms

Accuracy

43.4% (12.2b remaining)

Error of 30.0b against oracle of 17.8b and baseline of 39.3b

bsearch60.0ms

Steps

Iters	Range	Point
7	4.551559100072214e+119	6.772110124095701e+121	5.02207224652285e+121
10	3.422563478738447e-149	2.031606712727549e-138	6.302573219147232e-144
4	-1.4612837306014034e-101	-8.832668315785913e-102	-9.359301584479851e-102

Iters

Range

Point

4.551559100072214e+119

6.772110124095701e+121

5.02207224652285e+121

3.422563478738447e-149

2.031606712727549e-138

6.302573219147232e-144

-1.4612837306014034e-101

-8.832668315785913e-102

-9.359301584479851e-102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample973.0ms

Algorithm

intervals

Results

284.0ms	6044×	body	80	valid
187.0ms	691×	body	2560	valid
110.0ms	481×	body	1280	valid
94.0ms	268×	body	5120	valid
49.0ms	283×	body	640	valid
23.0ms	158×	body	320	valid
7.0ms	75×	body	160	valid

Details

sample38.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite19.0ms

series38.0ms

simplify71.0ms

prune97.0ms

localize13.0ms

rewrite44.0ms

series25.0ms

simplify47.0ms

prune129.0ms

localize20.0ms

rewrite32.0ms

series26.0ms

simplify107.0ms

prune124.0ms

localize6.0ms

rewrite6.0ms

series10.0ms

simplify62.0ms

prune25.0ms

regimes228.0ms

bsearch60.0ms

simplify2.0ms

end0.0ms

sample973.0ms

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