Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	192×	body	80	valid
5.0ms	24×	body	2560	valid
3.0ms	19×	body	1280	valid
1.0ms	11×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize14.0ms

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)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `fma-def` `diff-log` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
29.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
167.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune230.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.5b	(- (hypot re im) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

10.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
3.0ms	(- (hypot re im) re)

series240.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
59.0ms	(- (hypot re im) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	273	321
1	1082	232
2	5001	228

prune121.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
15.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `sqrt-div` `associate-r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

2 → 25

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series376.0ms

Counts

2 → 6

Calls

2 calls:

239.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
137.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify35.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	192	304
1	720	267
2	5001	251

prune114.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
11.2b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
0.0ms	(cbrt (hypot re im))
14.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series394.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (hypot re im))
114.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
58.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify93.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	167	446
1	570	322
2	2968	294
3	5001	292

prune251.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

regimes112.0ms

Accuracy

30.4% (4.1b remaining)

Error of 11.6b against oracle of 7.5b and baseline of 13.4b

bsearch146.0ms

Steps

Iters	Range		Point
7	9.739044821180595e+118	3.475160617912536e+120	1.0065728139945699e+120
9	5.673786592152021e+50	1.3343555727371729e+56	1.753869160177844e+51
7	5.3209797468654447e-20	1.0947205305537269e-17	1.0740812147784067e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	38	28
1	45	14
2	48	14
3	48	14

end0.0ms

sample700.0ms

Algorithm

intervals

Results

214.0ms	5992×	body	80	valid
139.0ms	682×	body	2560	valid
78.0ms	486×	body	1280	valid
72.0ms	292×	body	5120	valid
39.0ms	304×	body	640	valid
17.0ms	174×	body	320	valid
4.0ms	70×	body	160	valid