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)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
20.0ms	(- (sqrt (+ (* re re) (* im im))) re)
19.0ms	(sqrt (+ (* re re) (* im im)))

series246.0ms

Counts

3 → 9

Calls

3 calls:

164.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	277	577
1	946	551
2	3328	541
3	5001	540

prune182.0ms

Filtered

73 candidates to 52 candidates (71.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 18.7b

Counts

74 → 6

localize13.0ms

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)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

238×	`sqrt-prod`
166×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
71×	`associate-l`
62×	`distribute-lft-out`
61×	`swap-sqr`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`difference-of-squares`
18×	`add-cube-cbrt` `pow1/2` `unswap-sqr`
14×	`associate-r`
9×	`pow-prod-up`
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/` `*-commutative` `distribute-lft-out--`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `flip--` `cbrt-unprod`

Counts

4 → 193

Calls

4 calls:

46.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
68.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
47.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	275	1581
1	885	1452
2	5002	1428

prune289.0ms

Filtered

205 candidates to 76 candidates (37.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	205	6	211

Merged error: 18.7b

Counts

211 → 6

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

143×	`sqrt-prod`
141×	`add-sqr-sqrt`
62×	`unswap-sqr`
51×	`*-un-lft-identity`
46×	`difference-of-squares`
28×	`associate-r`
10×	`swap-sqr`
9×	`associate-l`
7×	`pow1` `add-cube-cbrt`
5×	`*-commutative` `distribute-lft-out` `add-log-exp`
4×	`sqrt-div` `distribute-lft-out--`
3×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `flip-+`

Counts

3 → 108

Calls

3 calls:

57.0ms	(sqrt (* 2.0 (- (* (sqrt (sqrt (* 1 1))) (sqrt (+ (* re re) (* im im)))) re)))
54.0ms	(- (* (sqrt (sqrt (* 1 1))) (sqrt (+ (* re re) (* im im)))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(sqrt (* 2.0 (- (* (sqrt (sqrt (* 1 1))) (sqrt (+ (* re re) (* im im)))) re)))
48.0ms	(- (* (sqrt (sqrt (* 1 1))) (sqrt (+ (* re re) (* im im)))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	394	1687
1	1167	1578
2	4380	1494
3	5001	1492

prune206.0ms

Filtered

117 candidates to 52 candidates (44.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	117	6	123

Merged error: 18.7b

Counts

123 → 6

localize21.0ms

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)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
32×	`sqrt-prod`
20×	`distribute-lft-out`
16×	`associate-l`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `sqrt-div` `swap-sqr`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

20.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify154.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	92	476
1	223	464
2	539	464
3	1396	464
4	4413	464
5	5002	464

prune305.0ms

Filtered

92 candidates to 60 candidates (65.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Merged error: 18.7b

Counts

98 → 6

regimes157.0ms

Accuracy

59.7% (8.4b remaining)

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

bsearch81.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	51	26
2	51	26

end0.0ms

sample685.0ms

Algorithm

intervals

Results

208.0ms	6021×	body	80	valid
138.0ms	723×	body	2560	valid
80.0ms	479×	body	1280	valid
71.0ms	292×	body	5120	valid
33.0ms	273×	body	640	valid
13.0ms	144×	body	320	valid
4.0ms	68×	body	160	valid