Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
4.0ms	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

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

rewrite62.0ms

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))
31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

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

prune241.0ms

Filtered

100 candidates to 72 candidates (72.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
0.5b	(- (hypot re im) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

25.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
3.0ms	(- (hypot re im) re)

series241.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
60.0ms	(- (hypot re im) re)

simplify32.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	232	325
1	856	239
2	5002	235

prune122.0ms

Filtered

50 candidates to 37 candidates (74.0%)

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 (* 1 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))))
15.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
3×	`sqrt-pow1` `pow-prod-down`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `sqrt-prod` `fma-udef`

Counts

2 → 24

Calls

2 calls:

6.0ms	(sqrt (* 2.0 (* 1 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series381.0ms

Counts

2 → 6

Calls

2 calls:

239.0ms	(sqrt (* 2.0 (* 1 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))))
142.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify59.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	140	261
1	459	227
2	2028	215
3	5001	210

prune107.0ms

Filtered

30 candidates to 25 candidates (83.3%)

Pruning

8 alts after pruning (7 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)

rewrite16.0ms

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:

114.0ms	(cbrt (hypot re im))
109.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
60.0ms	(- (* (* (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 (88.0ms)

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

prune245.0ms

Filtered

69 candidates to 59 candidates (85.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.8b

regimes119.0ms

Accuracy

30.4% (4.1b remaining)

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

bsearch144.0ms

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	40	28
1	47	14
2	50	14
3	50	14

end0.0ms

sample656.0ms

Algorithm

intervals

Results

194.0ms	5992×	body	80	valid
125.0ms	682×	body	2560	valid
74.0ms	292×	body	5120	valid
73.0ms	486×	body	1280	valid
36.0ms	304×	body	640	valid
20.0ms	174×	body	320	valid
4.0ms	70×	body	160	valid