Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	20×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize10.0ms

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)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `fma-def` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `hypot-def` `distribute-lft-out`

Counts

4 → 67

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
185.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune230.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.8b	(+ re (hypot re im))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
5×	`*-un-lft-identity`
4×	`associate-*r/` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `sqrt-pow1` `pow-prod-down`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 33

Calls

2 calls:

10.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
3.0ms	(+ re (hypot re im))

series257.0ms

Counts

2 → 6

Calls

2 calls:

197.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
61.0ms	(+ re (hypot re im))

simplify82.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	194	185
1	791	167
2	3233	161
3	5001	161

prune116.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
0.4b	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))
0.8b	(+ re (hypot re im))
0.8b	(+ re (hypot re im))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

148×	`sqrt-pow1`
146×	`pow1`
76×	`pow-prod-down`
31×	`sqrt-prod`
30×	`associate-*r/`
28×	`add-sqr-sqrt` `sqrt-div`
22×	`pow1/2`
21×	`pow-prod-up`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`pow-sqr`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `associate-*l/` `sum-log` `distribute-lft-out`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 154

Calls

4 calls:

12.0ms	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
79.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))
2.0ms	(+ re (hypot re im))
3.0ms	(+ re (hypot re im))

series558.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
197.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))
63.0ms	(+ re (hypot re im))
58.0ms	(+ re (hypot re im))

simplify66.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	408	1059
1	1919	954
2	5001	921

prune372.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
16.3b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt re)
5.0ms	(cbrt re)
1.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

series746.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt re)
182.0ms	(cbrt re)
182.0ms	(cbrt re)
190.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	60	220
1	121	195
2	359	187
3	1734	185
4	5001	185

prune203.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.7b

regimes197.0ms

Accuracy

-8.5% (6.8b remaining)

Error of 14.5b against oracle of 7.6b and baseline of 13.9b

bsearch181.0ms

Steps

Iters	Range		Point
7	669068328165.988	122937128512558.11	1629294977609.3977
10	2.2020631136780537e-106	4.626226025066689e-90	2.969008484960743e-98
7	-1.6028447693892302e-70	-9.28747149766958e-72	-1.4219463292392273e-70
8	-2.7139041588347048e+32	-1.903026018846269e+29	-3.424014799259077e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	45
1	60	45
2	60	45

end0.0ms

sample656.0ms

Algorithm

intervals

Results

199.0ms	5965×	body	80	valid
135.0ms	712×	body	2560	valid
83.0ms	529×	body	1280	valid
61.0ms	266×	body	5120	valid
35.0ms	290×	body	640	valid
14.0ms	160×	body	320	valid
5.0ms	78×	body	160	valid