Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	28×	body	2560	valid
2.0ms	16×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune147.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 18.7b

Counts

53 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.2b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
46.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune287.0ms

Filtered

138 candidates to 75 candidates (54.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Merged error: 18.7b

Counts

144 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (- (* (sqrt 1) (sqrt (+ (* re re) (* im im)))) re)))
1.0b	(- (* (sqrt 1) (sqrt (+ (* re re) (* im im)))) re)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

10.0ms	(sqrt (* 2.0 (- (* (sqrt 1) (sqrt (+ (* re re) (* im im)))) re)))
9.0ms	(- (* (sqrt 1) (sqrt (+ (* re re) (* im im)))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(sqrt (* 2.0 (- (* (sqrt 1) (sqrt (+ (* re re) (* im im)))) re)))
47.0ms	(- (* (sqrt 1) (sqrt (+ (* re re) (* im im)))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	245	422
1	822	382
2	2950	373
3	5002	370

prune150.0ms

Filtered

49 candidates to 40 candidates (81.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	49	6	55

Merged error: 18.7b

Counts

55 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify141.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (135.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune305.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 18.7b

Counts

78 → 6

regimes139.0ms

Accuracy

59.7% (8.4b remaining)

Error of 26.0b against oracle of 17.6b and baseline of 38.5b

bsearch79.0ms

Steps

Iters	Range		Point
9	-6.547406122260382e-303	-6.7102388536115e-309	-7.119203138679085e-309
6	-3.245969229886643e+141	-4.4689590379865175e+140	-5.416049338382167e+140

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	25
1	47	25

end0.0ms

sample685.0ms

Algorithm

intervals

Results

203.0ms	6021×	body	80	valid
148.0ms	723×	body	2560	valid
79.0ms	479×	body	1280	valid
69.0ms	292×	body	5120	valid
34.0ms	273×	body	640	valid
13.0ms	144×	body	320	valid
4.0ms	68×	body	160	valid