Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	186×	body	80	valid
5.0ms	26×	body	2560	valid
3.0ms	12×	body	5120	valid
3.0ms	18×	body	1280	valid
1.0ms	5×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	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: 41.6b

localize10.0ms

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)
32.6b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

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:

29.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
25.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series258.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

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

prune186.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.4b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

0.0ms	(hypot re im)
10.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
3.0ms	(- (hypot re im) re)

series288.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(hypot re im)
185.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
57.0ms	(- (hypot re im) re)

simplify136.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	231	336
1	764	242
2	4704	227
3	5001	217

prune155.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.3b

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)

rewrite51.0ms

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:

4.0ms	(sqrt (sqrt (* 2.0 (- (hypot re im) re))))
35.0ms	(* (sqrt (sqrt (* 2.0 (- (hypot re im) re)))) (sqrt (sqrt (* 2.0 (- (hypot re im) re)))))
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)

series531.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(sqrt (sqrt (* 2.0 (- (hypot re im) re))))
185.0ms	(* (sqrt (sqrt (* 2.0 (- (hypot re im) re)))) (sqrt (sqrt (* 2.0 (- (hypot re im) re)))))
58.0ms	(- (hypot re im) re)
56.0ms	(- (hypot re im) re)

simplify67.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (54.0ms)

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

prune373.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (hypot re im) re))
0.5b	(- (hypot re im) re)
0.5b	(- (hypot re im) re)
0.5b	(- (hypot re im) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

2.0ms	(cbrt (- (hypot re im) re))
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)

series326.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (- (hypot re im) re))
58.0ms	(- (hypot re im) re)
55.0ms	(- (hypot re im) re)
58.0ms	(- (hypot re im) re)

simplify109.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	226	736
1	690	507
2	3777	474
3	5001	444

prune289.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.3b

regimes77.0ms

Accuracy

13.9% (4.8b remaining)

Error of 12.1b against oracle of 7.2b and baseline of 12.9b

bsearch71.0ms

Steps

Iters	Range		Point
10	7.616577456358012e+226	8.0887524214285465e+242	1.0935003992856566e+227

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample679.0ms

Algorithm

intervals

Results

204.0ms	6098×	body	80	valid
136.0ms	696×	body	2560	valid
79.0ms	472×	body	1280	valid
63.0ms	250×	body	5120	valid
31.0ms	256×	body	640	valid
14.0ms	149×	body	320	valid
5.0ms	79×	body	160	valid