Details

analyze326.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample32.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
7.0ms	26×	body	2560	valid
4.0ms	16×	body	1280	valid
2.0ms	6×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 40.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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)
7.0ms	(sqrt (+ (* re re) (* im im)))

series17.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5042	458

prune85.0ms

Filtered

38 candidates to 47 candidates (-23.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	6	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Merged error: 20.0b

Counts

48 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

9.6b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
32.0b	(sqrt (+ (* re re) (* im im)))
32.0b	(sqrt (+ (* re re) (* im im)))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

21.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5310	612

prune103.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	68	7	75

Merged error: 20.0b

Counts

75 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

14.5b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
32.0b	(sqrt (+ (* re re) (* im im)))
32.0b	(sqrt (+ (* re re) (* im im)))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

25.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5148	612

prune110.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	69	6	75

Merged error: 20.0b

Counts

75 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (sqrt (+ (* re re) (* im im))) re)
5.7b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
23.8b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
21.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4947	1144
1	4947	1144

prune98.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	80	8	88

Merged error: 16.0b

Counts

88 → 8

regimes251.0ms

Accuracy

48.4% (13.5b remaining)

Error of 28.5b against oracle of 15.0b and baseline of 41.1b

bsearch53.0ms

Steps

Iters	Range	Point
9	5.983163384489359e-27	9.413377566249406e-22	6.484290788128597e-27
6	-2.2414479971788564e-256	-5.197495970254032e-257	-7.599282262320009e-257
6	-2.79678333037385e+173	-6.260661590034211e+172	-6.362988283858864e+172

Iters

Range

Point

5.983163384489359e-27

9.413377566249406e-22

6.484290788128597e-27

-2.2414479971788564e-256

-5.197495970254032e-257

-7.599282262320009e-257

-2.79678333037385e+173

-6.260661590034211e+172

-6.362988283858864e+172

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	59
1	59	59

end0.0ms

sample887.0ms

Algorithm

intervals

Results

282.0ms	6073×	body	80	valid
189.0ms	672×	body	2560	valid
113.0ms	504×	body	1280	valid
87.0ms	267×	body	5120	valid
49.0ms	270×	body	640	valid
18.0ms	139×	body	320	valid
7.0ms	75×	body	160	valid

Details

analyze326.0ms

sample32.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite19.0ms

series17.0ms

simplify38.0ms

prune85.0ms

localize17.0ms

rewrite34.0ms

series24.0ms

simplify50.0ms

prune103.0ms

localize20.0ms

rewrite39.0ms

series24.0ms

simplify64.0ms

prune110.0ms

localize11.0ms

rewrite34.0ms

series46.0ms

simplify52.0ms

prune98.0ms

regimes251.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample887.0ms

Profiling