Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
4.0ms	21×	body	2560	valid
2.0ms	15×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	9×	body	640	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

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)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite118.0ms

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:

8.0ms	(+ (* re re) (* im im))
52.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (* re re) (* im im))
154.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(- (sqrt (+ (* re re) (* im im))) re)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

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

prune229.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.5b	(- (hypot re im) re)

rewrite30.0ms

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

Counts

2 → 43

Calls

2 calls:

22.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
6.0ms	(- (hypot re im) re)

series212.0ms

Counts

2 → 6

Calls

2 calls:

163.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
50.0ms	(- (hypot re im) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	273	321
1	1082	232
2	5001	228

prune117.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.4b	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
0.5b	(- (hypot re im) re)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

9.0ms	(sqrt (- (hypot re im) re))
24.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
6.0ms	(- (hypot re im) re)

series326.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(sqrt (- (hypot re im) re))
164.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
53.0ms	(- (hypot re im) re)

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	590
1	1250	494
2	5002	482

prune205.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
14.8b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite8.0ms

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` `sqrt-div` `associate-r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

2 → 25

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series336.0ms

Counts

2 → 6

Calls

2 calls:

211.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
125.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify35.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	192	304
1	720	267
2	5001	251

prune94.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

regimes159.0ms

Accuracy

-1.3% (6.2b remaining)

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

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	54
1	55	54
2	55	54

end0.0ms

sample694.0ms

Algorithm

intervals

Results

189.0ms	6010×	body	80	valid
130.0ms	705×	body	2560	valid
73.0ms	469×	body	1280	valid
66.0ms	288×	body	5120	valid
40.0ms	299×	body	640	valid
13.0ms	145×	body	320	valid
7.0ms	84×	body	160	valid