Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	199×	body	80	valid
5.0ms	23×	body	2560	valid
2.0ms	9×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	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: 38.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
5×	`hypot-def`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`+-commutative`
2×	`fma-def` `pow1/2` `associate-*r/` `sqrt-prod`

Counts

4 → 21

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
191.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
57.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	203	172
1	717	155
2	2348	142
3	5002	139

prune88.0ms

Filtered

33 candidates to 26 candidates (78.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	4	34

Merged error: 6.7b

Counts

34 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (hypot im re) re)))
0.7b	(+ (hypot im re) re)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `sqrt-div` `associate-*r/` `sqrt-prod` `flip-+`
1×	`+-commutative` `pow1/2` `*-commutative`

Counts

2 → 8

Calls

2 calls:

4.0ms	(sqrt (* 2.0 (+ (hypot im re) re)))
2.0ms	(+ (hypot im re) re)

series246.0ms

Counts

2 → 6

Calls

2 calls:

189.0ms	(sqrt (* 2.0 (+ (hypot im re) re)))
57.0ms	(+ (hypot im re) re)

simplify62.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	186	106
1	579	94
2	2283	86
3	5001	85

prune43.0ms

Filtered

14 candidates to 13 candidates (92.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	14	4	18

Merged error: 6.5b

Counts

18 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (hypot im re) re))
0.3b	(* (sqrt 2.0) (sqrt (+ (hypot im re) re)))
0.7b	(+ (hypot im re) re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
3×	`flip3-+` `pow1/2` `flip-+`
2×	`associate-*r/`
1×	`+-commutative` `sqrt-unprod` `pow-prod-down` `*-commutative`

Counts

3 → 11

Calls

3 calls:

2.0ms	(sqrt (+ (hypot im re) re))
8.0ms	(* (sqrt 2.0) (sqrt (+ (hypot im re) re)))
2.0ms	(+ (hypot im re) re)

series363.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(sqrt (+ (hypot im re) re))
188.0ms	(* (sqrt 2.0) (sqrt (+ (hypot im re) re)))
57.0ms	(+ (hypot im re) re)

simplify108.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	271	153
1	820	132
2	3819	120
3	5001	119

prune64.0ms

Filtered

20 candidates to 19 candidates (95.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	20	4	24

Merged error: 6.5b

Counts

24 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re)))))
0.7b	(- (hypot re im) re)
4.9b	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
22.1b	(/ (pow im 2) (- (hypot re im) re))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-*r/`
12×	`sqrt-div`
11×	`associate-r`
10×	`sqrt-prod`
6×	`associate-/r/` `associate-/l*`
5×	`clear-num`
4×	`flip3--` `flip--`
3×	`frac-2neg` `*-commutative` `div-inv` `unpow2` `sqr-pow`
2×	`un-div-inv`
1×	`sub-neg` `pow1/2`

Counts

4 → 35

Calls

4 calls:

6.0ms	(* 0.5 (sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re)))))
2.0ms	(- (hypot re im) re)
5.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
4.0ms	(/ (pow im 2) (- (hypot re im) re))

series622.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(* 0.5 (sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re)))))
65.0ms	(- (hypot re im) re)
212.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
88.0ms	(/ (pow im 2) (- (hypot re im) re))

simplify96.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	249	294
1	780	272
2	3395	256
3	5003	255

prune135.0ms

Filtered

47 candidates to 43 candidates (91.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	44	7	51

Merged error: 1.6b

Counts

51 → 7

regimes132.0ms

Accuracy

68.4% (3.4b remaining)

Error of 5.6b against oracle of 2.2b and baseline of 12.9b

bsearch30.0ms

Steps

Iters	Range		Point
6	7.524734755904856e-279	3.3407704314481424e-278	1.3940086170973382e-278

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	31	14
2	31	14

end0.0ms

sample696.0ms

Algorithm

intervals

Results

215.0ms	6077×	body	80	valid
136.0ms	666×	body	2560	valid
76.0ms	473×	body	1280	valid
71.0ms	293×	body	5120	valid
39.0ms	288×	body	640	valid
13.0ms	129×	body	320	valid
5.0ms	74×	body	160	valid