Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	15×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt` `sqrt-prod`
6×	`add-cube-cbrt` `fma-def`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out`

Counts

3 → 53

Calls

3 calls:

23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
35.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
42.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune181.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.6b	(+ re (hypot re im))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
5×	`*-un-lft-identity`
4×	`associate-*r/` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `sqrt-pow1` `pow-prod-down`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 33

Calls

2 calls:

26.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
6.0ms	(+ re (hypot re im))

series236.0ms

Counts

2 → 6

Calls

2 calls:

183.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
53.0ms	(+ re (hypot re im))

simplify81.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	194	185
1	791	167
2	3233	161
3	5001	161

prune122.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
0.4b	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))
0.6b	(+ re (hypot re im))
0.6b	(+ re (hypot re im))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

148×	`sqrt-pow1`
146×	`pow1`
76×	`pow-prod-down`
31×	`sqrt-prod`
30×	`associate-*r/`
28×	`add-sqr-sqrt` `sqrt-div`
22×	`pow1/2`
21×	`pow-prod-up`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`pow-sqr`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `associate-*l/` `sum-log` `distribute-lft-out`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 154

Calls

4 calls:

22.0ms	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
158.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))
5.0ms	(+ re (hypot re im))
6.0ms	(+ re (hypot re im))

series506.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
183.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))
57.0ms	(+ re (hypot re im))
52.0ms	(+ re (hypot re im))

simplify71.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	408	1059
1	1919	954
2	5001	921

prune378.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ re (hypot re im))
0.6b	(+ re (hypot re im))
0.6b	(+ re (hypot re im))
0.7b	(pow (cbrt (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))) 4)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down` `add-log-exp`
9×	`fma-def`
7×	`cbrt-prod`
5×	`pow1` `add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative` `pow-unpow` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
2×	`pow-pow`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

9.0ms	(+ re (hypot re im))
5.0ms	(+ re (hypot re im))
5.0ms	(+ re (hypot re im))
9.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))) 4)

series587.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ re (hypot re im))
51.0ms	(+ re (hypot re im))
58.0ms	(+ re (hypot re im))
421.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))) 4)

simplify140.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (132.0ms)

Iter	Nodes	Cost
0	312	567
1	1055	529
2	4450	520
3	5001	517

prune398.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

regimes236.0ms

Accuracy

31% (4.2b remaining)

Error of 11.4b against oracle of 7.2b and baseline of 13.3b

bsearch55.0ms

Steps

Iters	Range		Point
9	-1.2163543548218358e+117	-2.505330959308098e+109	-1.1118756429176863e+114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	30	13
2	30	13

end0.0ms

sample691.0ms

Algorithm

intervals

Results

186.0ms	6027×	body	80	valid
130.0ms	692×	body	2560	valid
86.0ms	516×	body	1280	valid
59.0ms	267×	body	5120	valid
35.0ms	280×	body	640	valid
13.0ms	147×	body	320	valid
4.0ms	71×	body	160	valid