Details

sample39.0ms

Algorithm

intervals

Results

9.0ms	201×	body	80	valid
9.0ms	20×	body	2560	valid
2.0ms	10×	body	640	valid
2.0ms	10×	body	1280	valid
2.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	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

prune4.0ms

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: 37.5b

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)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* re re) (* im im))
237.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (86.0ms)

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

prune259.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 14.9b

Counts

64 → 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)))))
7.2b	(+ (* (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)))

rewrite40.0ms

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:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms	(+ (* (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)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
50.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

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

prune386.0ms

Filtered

136 candidates to 75 candidates (55.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	135	7	142

Merged error: 14.9b

Counts

142 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
11.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
428.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	324	640
1	1367	605
2	5002	595

prune297.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	81	9	90

Merged error: 14.9b

Counts

90 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
10.2b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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:

7.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
16.0ms	(+ (* (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)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
48.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (43.0ms)

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

prune372.0ms

Filtered

103 candidates to 66 candidates (64.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	103	9	112

Merged error: 14.9b

Counts

112 → 9

regimes306.0ms

Accuracy

42.1% (12.5b remaining)

Error of 29.8b against oracle of 17.3b and baseline of 38.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	52
1	52	52

end0.0ms

sample963.0ms

Algorithm

intervals

Results

282.0ms	6056×	body	80	valid
190.0ms	683×	body	2560	valid
108.0ms	473×	body	1280	valid
92.0ms	282×	body	5120	valid
51.0ms	291×	body	640	valid
19.0ms	143×	body	320	valid
6.0ms	72×	body	160	valid

Details

sample39.0ms

simplify4.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series345.0ms

simplify92.0ms

prune259.0ms

localize13.0ms

rewrite40.0ms

series158.0ms

simplify48.0ms

prune386.0ms

localize11.0ms

rewrite31.0ms

series539.0ms

simplify41.0ms

prune297.0ms

localize16.0ms

rewrite34.0ms

series226.0ms

simplify54.0ms

prune372.0ms

regimes306.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample963.0ms

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