Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	15×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

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: 41.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

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:

22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (64.0ms)

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

prune157.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.1b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.5b	(sqrt (+ (* re re) (* im im)))
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

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:

52.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
30.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

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

prune296.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
3.8b	(exp (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

28.0ms	(log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
27.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
86.0ms	(exp (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))
47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
165.0ms	(exp (log (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify103.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	359	711
1	1067	644
2	3676	620
3	5001	614

prune248.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

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:

22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (63.0ms)

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

prune119.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.9b

regimes572.0ms

Accuracy

56.9% (9.0b remaining)

Error of 26.7b against oracle of 17.7b and baseline of 38.6b

bsearch76.0ms

Steps

Iters	Range		Point
10	5.021239776809263e+39	2.034575374228523e+56	1.9187886873923672e+56
7	-3.866095542241674e-287	-7.929187368858259e-289	-8.0180108365289025e-289

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	22
1	37	22

end0.0ms

sample692.0ms

Algorithm

intervals

Results

190.0ms	6027×	body	80	valid
128.0ms	692×	body	2560	valid
77.0ms	516×	body	1280	valid
65.0ms	267×	body	5120	valid
38.0ms	280×	body	640	valid
13.0ms	147×	body	320	valid
4.0ms	71×	body	160	valid