Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	196×	body	80	valid
8.0ms	23×	body	2560	valid
4.0ms	4×	body	5120	valid
4.0ms	16×	body	640	valid
3.0ms	10×	body	1280	valid
1.0ms	5×	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: 40.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

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:

3.0ms	(+ (* re re) (* im im))
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)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
170.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(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

prune237.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.3b	(- (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×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`sub-neg` `hypot-udef` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `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) 0)))
3.0ms	(- (hypot re im) re)

series284.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(hypot re im)
183.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
56.0ms	(- (hypot re im) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	283	345
1	1118	247
2	5001	236

prune164.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.0b	(hypot re im)
0.3b	(- (hypot re im) re)
0.4b	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
17×	`sqrt-prod`
16×	`add-cube-cbrt`
9×	`pow1` `prod-diff`
8×	`associate-r`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `hypot-udef` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

5.0ms	(sqrt (- (hypot re im) re))
0.0ms	(hypot re im)
5.0ms	(- (hypot re im) re)
13.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (- (hypot re im) re))
46.0ms	(hypot re im)
55.0ms	(- (hypot re im) re)
181.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	348	614
1	1286	509
2	5001	488

prune253.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (hypot re im) re)
0.4b	(* (fabs (cbrt (- (hypot re im) re))) (sqrt 2.0))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`add-cube-cbrt`
10×	`cbrt-prod`
9×	`prod-diff`
6×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-div` `sqrt-prod` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `associate-l` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

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

series396.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (hypot re im) re)
33.0ms	(* (fabs (cbrt (- (hypot re im) re))) (sqrt 2.0))
151.0ms	(cbrt (- (hypot re im) re))
154.0ms	(cbrt (- (hypot re im) re))

simplify125.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	300	699
1	970	587
2	4769	564
3	5001	563

prune312.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

regimes120.0ms

Accuracy

18.3% (5.0b remaining)

Error of 12.4b against oracle of 7.4b and baseline of 13.5b

bsearch202.0ms

Steps

Iters	Range		Point
7	1.5121775450301864e+201	2.4897702333233588e+203	1.0003561765365922e+202
10	8.815605325869767e-16	0.0002199982819353488	6.396566414275417e-05
9	1.4092599498627254e-49	4.735819680718145e-43	1.0542686008392895e-44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	38	28
1	45	14
2	48	14
3	48	14

end0.0ms

sample1.2s

Algorithm

intervals

Results

418.0ms	5992×	body	80	valid
251.0ms	708×	body	2560	valid
149.0ms	517×	body	1280	valid
116.0ms	278×	body	5120	valid
62.0ms	272×	body	640	valid
26.0ms	150×	body	320	valid
11.0ms	83×	body	160	valid