Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize13.0ms

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)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
177.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune192.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
3.6b	(exp (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
16.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(exp (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
176.0ms	(exp (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	289	585
1	832	545
2	2405	511
3	5002	503

prune221.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
3.8b	(pow E (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
14.0ms	(pow E (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
854.0ms	(pow E (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	382	742
1	1122	697
2	3690	669
3	5002	651

prune245.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow E (log (sqrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))
3.2b	(pow E (log (sqrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))
27.5b	(sqrt (+ (* re re) (* im im)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `pow-unpow`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`unpow-prod-up` `add-cube-cbrt` `log-prod` `*-un-lft-identity` `sqrt-pow1`
12×	`sqrt-div` `log-pow`
6×	`add-exp-log` `unpow-prod-down` `pow1/2`
4×	`log-div` `flip3-+` `associate-*r/` `pow-exp` `add-cbrt-cube` `flip-+` `pow-sub` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `pow-prod-down` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

15.0ms	(pow E (log (sqrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))
15.0ms	(pow E (log (sqrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(pow E (log (sqrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))
283.0ms	(pow E (log (sqrt (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))))
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify120.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	388	1190
1	1153	1164
2	4360	1136
3	5001	1104

prune421.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.0b

regimes560.0ms

Accuracy

59.2% (8.5b remaining)

Error of 26.4b against oracle of 17.9b and baseline of 38.8b

bsearch111.0ms

Steps

Iters	Range		Point
11	5.10808278574109e+145	3.366560557353129e+171	2.074955054900539e+149
7	2.1468477792754155e-253	3.535306663239892e-252	5.230447706929968e-253
7	2.00818341296373e-296	3.449635196547704e-295	2.409964474129751e-295

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	26
1	48	26

end0.0ms

sample681.0ms

Algorithm

intervals

Results

205.0ms	6047×	body	80	valid
132.0ms	681×	body	2560	valid
77.0ms	483×	body	1280	valid
68.0ms	272×	body	5120	valid
41.0ms	286×	body	640	valid
14.0ms	144×	body	320	valid
9.0ms	87×	body	160	valid