Details

sample46.0ms

Algorithm

intervals

Results

22.0ms	214×	body	80	valid
5.0ms	13×	body	2560	valid
4.0ms	7×	body	5120	valid
3.0ms	8×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`*-un-lft-identity`
4×	`pow1` `add-cube-cbrt` `sqrt-prod`
3×	`add-exp-log` `add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 41

Calls

3 calls:

3.0ms	(+ (* re re) (* im im))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	172	305
1	661	282
2	1936	278
3	5002	276

prune145.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.4b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
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×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

29.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
18.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
46.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune306.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.8b

localize17.0ms

Local error

Found 4 expressions with local error:

5.3b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
6.4b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp`
4×	`add-exp-log` `log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-cbrt-cube`
2×	`rem-sqrt-square` `log-div` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `flip--` `flip-+` `difference-of-squares`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

28.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
18.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
51.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify112.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (104.0ms)

Iter	Nodes	Cost
0	191	746
1	442	597
2	1109	556
3	3525	548
4	5002	542

prune270.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.8b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `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)))

series154.0ms

Counts

1 → 3

Calls

1 calls:

154.0ms

(sqrt (* 2.0 (- im re)))

simplify48.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	135	103
1	403	90
2	1463	79
3	5002	76

prune34.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 14.8b

regimes449.0ms

Accuracy

52.5% (9.8b remaining)

Error of 28.1b against oracle of 18.3b and baseline of 38.9b

bsearch370.0ms

Steps

Iters	Range		Point
7	1.8766978185172877e+88	3.047530528666286e+89	1.9016733895639456e+88
5	1.5896180358927368e+68	5.614762643511228e+68	5.491583371113908e+68
7	1.3006604657059154e-48	2.175174403907481e-46	1.3595218621366488e-48
8	1.933364594733743e-77	8.217386779769018e-74	9.620486412743379e-76
8	1.1247906893733106e-296	7.127760511990525e-292	1.6737151774934597e-296
10	-1.3754465060135574e-218	-3.5096784081435916e-233	-2.4133772973938416e-231
8	-8.932761495434891e+18	-152849402421631.16	-8.78998906857299e+18

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	54
1	66	54
2	72	54
3	78	54
4	87	54
5	100	54
6	112	54
7	119	54
8	120	54
9	120	54

end0.0ms

sample1.4s

Algorithm

intervals

Results

551.0ms	6000×	body	80	valid
304.0ms	728×	body	2560	valid
174.0ms	478×	body	1280	valid
147.0ms	301×	body	5120	valid
75.0ms	268×	body	640	valid
29.0ms	138×	body	320	valid
15.0ms	87×	body	160	valid