Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	13×	body	1280	valid
1.0ms	6×	body	5120	valid
1.0ms	10×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

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)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
20.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series280.0ms

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)))

simplify91.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune189.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (+ (* re re) (* im im))) re)
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (76.0ms)

Iter	Nodes	Cost
0	135	456
1	332	432
2	839	424
3	2503	422
4	5002	420

prune235.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
15.9b	(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod` `sqrt-prod`
6×	`sqrt-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `associate-*r/`
3×	`pow-unpow` `flip3--` `sqrt-pow1` `flip--`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `flip3-+` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `flip-+` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

13.0ms	(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
7.0ms	(sqrt (+ (* re re) (* im im)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

464.0ms	(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
171.0ms	(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	426	918
1	1635	878
2	5001	860

prune250.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (+ (* re re) (* im im))) re)
4.4b	(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
15.9b	(cbrt (pow (sqrt (* 2.0 (exp (log (- (sqrt (+ (* re re) (* im im))) re))))) 3))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`cbrt-prod` `*-un-lft-identity`
10×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`pow1` `log-prod` `exp-sum` `add-log-exp`
4×	`add-exp-log` `unpow-prod-down` `log-div` `exp-prod` `exp-diff` `sqrt-div` `cube-prod` `add-cbrt-cube` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`cube-div` `cbrt-div` `associate-*r/` `distribute-lft-out--`
1×	`cube-mult` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `diff-log` `unpow3` `log-pow` `rem-cbrt-cube` `flip-+` `rem-exp-log` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(cbrt (pow (sqrt (* 2.0 (exp (log (- (sqrt (+ (* re re) (* im im))) re))))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
51.0ms	(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
175.0ms	(cbrt (pow (sqrt (* 2.0 (exp (log (- (sqrt (+ (* re re) (* im im))) re))))) 3))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	362	856
1	1179	823
2	3962	797
3	5001	789

prune253.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 15.7b

regimes525.0ms

Accuracy

59.3% (8.6b remaining)

Error of 26.8b against oracle of 18.1b and baseline of 39.4b

bsearch103.0ms

Steps

Iters	Range		Point
7	2.1468477792754155e-253	3.535306663239892e-252	3.293868608372057e-252
7	2.00818341296373e-296	3.449635196547704e-295	9.194803090293717e-296
7	-6.579287999353623e+83	-2.1130938932944453e+82	-6.485144449769119e+83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	35
1	52	35

end0.0ms

sample676.0ms

Algorithm

intervals

Results

195.0ms	5967×	body	80	valid
132.0ms	692×	body	2560	valid
82.0ms	514×	body	1280	valid
70.0ms	303×	body	5120	valid
36.0ms	288×	body	640	valid
20.0ms	151×	body	320	valid
5.0ms	85×	body	160	valid