Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	22×	body	2560	valid
6.0ms	193×	body	80	valid
2.0ms	16×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

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:

8.0ms	(+ (* re re) (* im im))
23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* re re) (* im im))
166.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

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

prune186.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.1b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

54.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
29.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
47.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune486.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.4b

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
15.4b	(+ (* (sqrt (exp (log (sqrt (+ (* re re) (* im im)))))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

10.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(+ (* (sqrt (exp (log (sqrt (+ (* re re) (* im im)))))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
43.0ms	(+ (* (sqrt (exp (log (sqrt (+ (* re re) (* im im)))))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify115.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 4 (108.0ms)

Iter	Nodes	Cost
0	208	622
1	485	555
2	1193	507
3	3624	495
4	5003	493

prune276.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.4b

localize26.0ms

Local error

Found 4 expressions with local error:

6.2b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
15.4b	(+ (* (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
31.1b	(log (+ (* re re) (* im im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

10.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
32.0ms	(+ (* (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(log (+ (* re re) (* im im)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
139.0ms	(+ (* (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
33.0ms	(sqrt (+ (* re re) (* im im)))
49.0ms	(log (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	294	738
1	817	652
2	2641	647
3	5002	647

prune284.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.4b

regimes183.0ms

Accuracy

55% (9.6b remaining)

Error of 27.0b against oracle of 17.4b and baseline of 38.7b

bsearch110.0ms

Steps

Iters	Range	Point
9	1.6564934462005338e+19	3.0077710628296854e+26	2.9712800106749567e+26
9	5.071879329881285e-240	1.4578539957000644e-231	1.0143613516873226e-237
7	-7.39486344966426e-262	-3.8712513553988877e-264	-6.682218147655113e-264

Iters

Range

Point

1.6564934462005338e+19

3.0077710628296854e+26

2.9712800106749567e+26

5.071879329881285e-240

1.4578539957000644e-231

1.0143613516873226e-237

-7.39486344966426e-262

-3.8712513553988877e-264

-6.682218147655113e-264

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	35
1	61	35
2	61	35

end0.0ms

sample702.0ms

Algorithm

intervals

Results

203.0ms	6053×	body	80	valid
127.0ms	655×	body	2560	valid
74.0ms	477×	body	1280	valid
64.0ms	283×	body	5120	valid
34.0ms	282×	body	640	valid
15.0ms	164×	body	320	valid
5.0ms	86×	body	160	valid