Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
3.0ms	15×	body	2560	valid
3.0ms	11×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	10×	body	640	valid
1.0ms	6×	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: 34.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series259.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.4b

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)

rewrite34.0ms

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:

29.0ms	(sqrt (* 2.0 (* 1 (- (hypot re im) re))))
3.0ms	(- (hypot re im) re)

series242.0ms

Counts

2 → 6

Calls

2 calls:

182.0ms	(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 (28.0ms)

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

prune137.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

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)))))
13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite8.0ms

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)))))
1.0ms	(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)))))
141.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify58.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (54.0ms)

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

prune122.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
9.5b	(- (* (* (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)

series398.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (hypot re im))
109.0ms	(cbrt (hypot re im))
112.0ms	(cbrt (hypot re im))
60.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify91.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (86.0ms)

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

prune262.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.3b

regimes182.0ms

Accuracy

-4% (5.8b remaining)

Error of 13.2b against oracle of 7.3b and baseline of 13.0b

bsearch86.0ms

Steps

Iters	Range		Point
8	1.085653884907432e-19	1.091098110926274e-15	1.969774278625561e-16
5	1.829737677608388e-73	7.00229751334036e-73	6.830376487536606e-73

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	14
1	41	14
2	41	14

end0.0ms

sample699.0ms

Algorithm

intervals

Results

215.0ms	6068×	body	80	valid
144.0ms	700×	body	2560	valid
77.0ms	438×	body	1280	valid
69.0ms	281×	body	5120	valid
39.0ms	276×	body	640	valid
16.0ms	163×	body	320	valid
5.0ms	74×	body	160	valid