Details

sample26.0ms

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

prune2.0ms

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)))

rewrite36.0ms

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:

4.0ms	(+ (* re re) (* im im))
14.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
11.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
173.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (37.0ms)

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

prune228.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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:

10.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series240.0ms

Counts

2 → 6

Calls

2 calls:

184.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
56.0ms	(- (hypot re im) re)

simplify129.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (124.0ms)

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

prune115.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
15.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 23

Calls

2 calls:

3.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series384.0ms

Counts

2 → 6

Calls

2 calls:

244.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
140.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify50.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	135	250
1	408	217
2	1603	205
3	5001	200

prune99.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3)) (- re re))))
0.5b	(cbrt (hypot re im))
0.7b	(pow (cbrt (hypot re im)) 3)
10.7b	(fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
8×	`pow1`
6×	`unpow-prod-down` `cube-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `sqrt-pow1` `pow1/3` `sqrt-div` `associate-*r/`
1×	`cube-mult` `pow-to-exp` `flip3-+` `pow1/2` `unpow3` `pow-prod-down` `pow-exp` `sqrt-prod` `flip-+` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

7.0ms	(sqrt (* 2.0 (+ (fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3)) (- re re))))
1.0ms	(cbrt (hypot re im))
3.0ms	(pow (cbrt (hypot re im)) 3)
1.0ms	(fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3))

series468.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(sqrt (* 2.0 (+ (fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3)) (- re re))))
113.0ms	(cbrt (hypot re im))
91.0ms	(pow (cbrt (hypot re im)) 3)
91.0ms	(fma (/ (- re) 2) 2 (pow (cbrt (hypot re im)) 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	327	502
1	1223	454
2	5003	418

prune232.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

regimes110.0ms

Accuracy

30.4% (4.1b remaining)

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

bsearch143.0ms

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	36	26
1	41	13
2	44	13
3	44	13

end0.0ms

sample687.0ms

Algorithm

intervals

Results

206.0ms	5992×	body	80	valid
134.0ms	682×	body	2560	valid
75.0ms	486×	body	1280	valid
69.0ms	292×	body	5120	valid
42.0ms	304×	body	640	valid
16.0ms	174×	body	320	valid
4.0ms	70×	body	160	valid