Details

analyze330.0ms

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

sample35.0ms

Algorithm

intervals

Results

9.0ms	196×	body	80	valid
8.0ms	20×	body	2560	valid
3.0ms	15×	body	1280	valid
3.0ms	9×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	5×	body	320	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: 37.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (+ (* re re) (* im im))) re)
0.5b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

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:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify33.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4949	551
1	4949	551

prune104.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	9	50

Merged error: 15.1b

Counts

50 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (+ re (sqrt (+ (* re re) (* im im))))) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
0.5b	(sqrt (* 2.0 (* (sqrt (+ re (sqrt (+ (* re re) (* im im))))) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))))
28.9b	(sqrt (+ (* re re) (* im im)))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

36×	`sqrt-div`
33×	`sqrt-prod`
28×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`pow1`
14×	`add-cube-cbrt` `flip3-+` `flip-+`
13×	`sqrt-pow1`
12×	`associate-*r/`
11×	`pow1/2` `swap-sqr`
8×	`frac-times`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `pow-prod-down` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-up`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

16.0ms	(* (sqrt (+ re (sqrt (+ (* re re) (* im im))))) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
17.0ms	(sqrt (* 2.0 (* (sqrt (+ re (sqrt (+ (* re re) (* im im))))) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sqrt (+ re (sqrt (+ (* re re) (* im im))))) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
27.0ms	(sqrt (* 2.0 (* (sqrt (+ re (sqrt (+ (* re re) (* im im))))) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5115	1713

prune133.0ms

Filtered

72 candidates to 124 candidates (-72.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	124	9	133

Merged error: 15.1b

Counts

133 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ re (sqrt (+ (* re re) (* im im))))
0.5b	(sqrt (* 2.0 (exp (log (+ re (sqrt (+ (* re re) (* im im))))))))
4.5b	(exp (log (+ re (sqrt (+ (* re re) (* im im))))))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

5.0ms	(+ re (sqrt (+ (* re re) (* im im))))
9.0ms	(sqrt (* 2.0 (exp (log (+ re (sqrt (+ (* re re) (* im im))))))))
7.0ms	(exp (log (+ re (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ re (sqrt (+ (* re re) (* im im))))
23.0ms	(sqrt (* 2.0 (exp (log (+ re (sqrt (+ (* re re) (* im im))))))))
7.0ms	(exp (log (+ re (sqrt (+ (* re re) (* im im))))))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify35.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5120	785

prune115.0ms

Filtered

53 candidates to 70 candidates (-32.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	69	10	79

Merged error: 15.1b

Counts

79 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.1b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

11.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
9.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
8.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4936	784
1	4936	784

prune87.0ms

Filtered

53 candidates to 74 candidates (-39.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	74	10	84

Merged error: 14.9b

Counts

84 → 10

regimes936.0ms

Accuracy

52.4% (10.1b remaining)

Error of 27.1b against oracle of 17.1b and baseline of 38.2b

bsearch135.0ms

Steps

Iters	Range		Point
6	4.86565370840311e+119	2.1248752146791368e+120	9.207225632419575e+119
9	4.6447082010756145e-105	5.020583559746355e-97	4.7357972410850955e-105
9	4.684835665227363e-151	1.6264165778023557e-143	5.1160026767062117e-144
6	2.5358754208386477e-169	1.136980852007717e-168	2.7348232889716076e-169
8	-9.354752198870725e-300	-2.278206225330619e-303	-2.5723644386022114e-302

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	107
1	59	107

end0.0ms

analyze333.0ms

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

sample932.0ms

Algorithm

intervals

Results

300.0ms	6047×	body	80	valid
201.0ms	696×	body	2560	valid
121.0ms	516×	body	1280	valid
86.0ms	252×	body	5120	valid
48.0ms	260×	body	640	valid
21.0ms	151×	body	320	valid
9.0ms	78×	body	160	valid

Details

analyze330.0ms

sample35.0ms

simplify3.0ms

prune6.0ms

localize10.0ms

rewrite18.0ms

series38.0ms

simplify33.0ms

prune104.0ms

localize15.0ms

rewrite44.0ms

series46.0ms

simplify63.0ms

prune133.0ms

localize14.0ms

rewrite26.0ms

series45.0ms

simplify35.0ms

prune115.0ms

localize14.0ms

rewrite31.0ms

series43.0ms

simplify36.0ms

prune87.0ms

regimes936.0ms

bsearch135.0ms

simplify1.0ms

end0.0ms

analyze333.0ms

sample932.0ms

Profiling