Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
6.0ms	30×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	12×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	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: 39.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

14.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series264.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

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

prune196.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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` `flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

8.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series247.0ms

Counts

2 → 6

Calls

2 calls:

190.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
57.0ms	(- (hypot re im) re)

simplify132.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	221	312
1	728	227
2	4440	212
3	5001	202

prune121.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (- (hypot re im) re))))
0.4b	(* (sqrt (sqrt (* 2.0 (- (hypot re im) re)))) (sqrt (sqrt (* 2.0 (- (hypot re im) re)))))
0.5b	(- (hypot re im) re)
0.5b	(- (hypot re im) re)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `sqrt-prod`
28×	`sqrt-div`
27×	`add-cube-cbrt`
23×	`pow-prod-down`
20×	`pow1/2`
18×	`prod-diff`
16×	`associate-*r/`
14×	`pow-prod-up`
9×	`flip3--` `swap-sqr` `flip--`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-*l/` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

6.0ms	(sqrt (sqrt (* 2.0 (- (hypot re im) re))))
17.0ms	(* (sqrt (sqrt (* 2.0 (- (hypot re im) re)))) (sqrt (sqrt (* 2.0 (- (hypot re im) re)))))
4.0ms	(- (hypot re im) re)
4.0ms	(- (hypot re im) re)

series536.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(sqrt (sqrt (* 2.0 (- (hypot re im) re))))
186.0ms	(* (sqrt (sqrt (* 2.0 (- (hypot re im) re)))) (sqrt (sqrt (* 2.0 (- (hypot re im) re)))))
58.0ms	(- (hypot re im) re)
60.0ms	(- (hypot re im) re)

simplify71.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	434	1199
1	1828	970
2	5001	940

prune385.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.9b

localize19.0ms

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))
15.5b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite6.0ms

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:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series497.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (hypot re im))
118.0ms	(cbrt (hypot re im))
115.0ms	(cbrt (hypot re im))
145.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify134.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (129.0ms)

Iter	Nodes	Cost
0	84	329
1	188	287
2	663	279
3	3464	272
4	5001	263

prune282.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.9b

regimes81.0ms

Accuracy

24.6% (4.4b remaining)

Error of 11.9b against oracle of 7.5b and baseline of 13.3b

bsearch45.0ms

Steps

Iters	Range		Point
6	1.7254500888309536e+136	9.339102222384328e+136	2.1604853055976255e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample677.0ms

Algorithm

intervals

Results

206.0ms	6030×	body	80	valid
143.0ms	729×	body	2560	valid
70.0ms	450×	body	1280	valid
66.0ms	281×	body	5120	valid
33.0ms	268×	body	640	valid
14.0ms	156×	body	320	valid
7.0ms	86×	body	160	valid