Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
4.0ms	20×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	12×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 40.1b

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)
29.2b	(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:

5.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* re re) (* im im))
179.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (67.0ms)

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

prune87.0ms

Filtered

33 candidates to 26 candidates (78.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Merged error: 7.9b

Counts

34 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (hypot im re) re)))
0.6b	(+ (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)

series243.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(sqrt (* 2.0 (+ (hypot im re) re)))
61.0ms	(+ (hypot im re) re)

simplify66.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 3 (63.0ms)

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

prune47.0ms

Filtered

14 candidates to 14 candidates (100.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	14	3	17

Merged error: 7.9b

Counts

17 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

1.3b	(- (hypot re im) re)
5.5b	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
24.6b	(/ (pow im 2) (- (hypot re im) re))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 23

Calls

3 calls:

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))

series346.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(- (hypot re im) re)
202.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (hypot re im) re))))
83.0ms	(/ (pow im 2) (- (hypot re im) re))

simplify97.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	230	192
1	761	181
2	3376	173
3	5001	172

prune103.0ms

Filtered

32 candidates to 29 candidates (90.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	29	6	35

Merged error: 2.5b

Counts

35 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (hypot re im) re) im)
0.0b	(/ im (/ (- (hypot re im) re) im))
1.3b	(- (hypot re im) re)
5.5b	(sqrt (* 2.0 (/ im (/ (- (hypot re im) re) im))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-/r/`
8×	`sqrt-prod`
6×	`associate-r` `clear-num` `associate-/l/`
5×	`frac-2neg` `sqrt-div` `div-inv`
4×	`flip3--` `associate-*r/` `flip--`
2×	`associate-/r*`
1×	`sub-neg` `pow1/2` `div-sub` `un-div-inv` `*-commutative`

Counts

4 → 33

Calls

4 calls:

3.0ms	(/ (- (hypot re im) re) im)
4.0ms	(/ im (/ (- (hypot re im) re) im))
2.0ms	(- (hypot re im) re)
6.0ms	(sqrt (* 2.0 (/ im (/ (- (hypot re im) re) im))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (hypot re im) re) im)
84.0ms	(/ im (/ (- (hypot re im) re) im))
59.0ms	(- (hypot re im) re)
206.0ms	(sqrt (* 2.0 (/ im (/ (- (hypot re im) re) im))))

simplify114.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	268	239
1	943	228
2	4229	218
3	5001	217

prune114.0ms

Filtered

45 candidates to 40 candidates (88.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	46	5	51

Merged error: 1.3b

Counts

51 → 5

regimes62.0ms

Accuracy

57.3% (5.2b remaining)

Error of 6.3b against oracle of 1.1b and baseline of 13.4b

bsearch38.0ms

Steps

Iters	Range		Point
8	-3.666763002298925e-174	-3.262421321844347e-177	-7.669907494275288e-177

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample665.0ms

Algorithm

intervals

Results

201.0ms	6033×	body	80	valid
137.0ms	708×	body	2560	valid
72.0ms	470×	body	1280	valid
63.0ms	270×	body	5120	valid
39.0ms	302×	body	640	valid
14.0ms	152×	body	320	valid
4.0ms	65×	body	160	valid