Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	27×	body	2560	valid
6.0ms	189×	body	80	valid
4.0ms	15×	body	5120	valid
2.0ms	11×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

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

series258.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
16.3b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

10.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
9.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
38.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
44.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
222.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	291	581
1	814	525
2	2384	502
3	5002	493

prune213.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.0b

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b	(exp (log (sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
16.3b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(exp (log (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)
6.0ms	(sqrt (+ (* re re) (* im im)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(exp (log (sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))))
36.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
47.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	324	697
1	864	626
2	2450	587
3	5002	574

prune272.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

4.0ms

(sqrt (* 2.0 (+ im re)))

series86.0ms

Counts

1 → 3

Calls

1 calls:

86.0ms

(sqrt (* 2.0 (+ im re)))

simplify50.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	171	97
1	494	85
2	1748	77
3	5001	74

prune34.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.0b

regimes240.0ms

Accuracy

57.5% (11.6b remaining)

Error of 28.9b against oracle of 17.3b and baseline of 44.7b

bsearch162.0ms

Steps

Iters	Range		Point
9	7.17281110532117e-87	2.4031352105883027e-79	2.5128194406165944e-83
9	3.0392225227475977e-109	1.3149852974355796e-102	6.040976157237577e-106
8	8.759955465341852e-197	9.415971551391981e-194	1.7143375768306352e-196
8	4.592090908020972e-292	2.209994737107717e-288	1.8913803268467336e-289

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	59
1	57	59

end0.0ms

sample688.0ms

Algorithm

intervals

Results

197.0ms	6051×	body	80	valid
151.0ms	715×	body	2560	valid
75.0ms	305×	body	5120	valid
73.0ms	440×	body	1280	valid
38.0ms	253×	body	640	valid
15.0ms	156×	body	320	valid
5.0ms	80×	body	160	valid