Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	200×	body	80	valid
7.0ms	27×	body	2560	valid
3.0ms	10×	body	5120	valid
3.0ms	13×	body	1280	valid
1.0ms	5×	body	640	valid
0.0ms	1×	body	320	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

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: 37.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(- (sqrt (+ (* re re) (* im im))) re)
0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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:

4.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* re re) (* im im))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
176.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

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

prune162.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Merged error: 18.4b

Counts

67 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt (+ (* re re) (* im im))) re)
0.0b	(+ (* re re) (* im im))
0.4b	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`sqrt-prod`
13×	`*-un-lft-identity`
9×	`pow1` `add-cube-cbrt` `associate-r`
8×	`add-log-exp`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`sqrt-div` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(+ (* re re) (* im im))
15.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
32.0ms	(+ (* re re) (* im im))
179.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify136.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	691
1	1267	648
2	4889	633
3	5001	633

prune200.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 18.4b

Counts

93 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
0.3b	(* (sqrt 2.0) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
31.2b	(sqrt (+ (* re re) (* im im)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

50×	`sqrt-prod`
36×	`add-sqr-sqrt`
32×	`sqrt-div`
24×	`associate-r`
18×	`pow1` `*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/` `pow-prod-down`
7×	`flip3--` `sqrt-pow1` `pow1/2` `associate-l` `flip--`
6×	`unswap-sqr`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `flip3-+` `associate-l/` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 108

Calls

4 calls:

25.0ms	(* (* (sqrt 2.0) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
18.0ms	(* (sqrt 2.0) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (* (sqrt 2.0) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re)))) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
196.0ms	(* (sqrt 2.0) (sqrt (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	496	1517
1	1980	1352
2	5001	1330

prune332.0ms

Filtered

120 candidates to 81 candidates (67.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	120	7	127

Merged error: 18.4b

Counts

127 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
5.9b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.3b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

11.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
202.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
71.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune249.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	108	10	118

Merged error: 6.9b

Counts

118 → 10

regimes299.0ms

Accuracy

46.3% (16.8b remaining)

Error of 23.4b against oracle of 6.6b and baseline of 37.9b

bsearch288.0ms

Steps

Iters	Range		Point
9	4.800951932276634e+87	9.885888095165e+93	9.958460283323213e+87
5	1.3046890090986254e+19	2.9300307707156197e+19	1.3216056275352607e+19
6	1.892206502670164e-22	1.6633021246357823e-21	1.642281532727481e-21
9	2.1427013888630277e-91	3.597710531849723e-82	2.3261881441599813e-91
10	-3.1136157660574424e-170	-9.966042788984376e-183	-3.080011509737395e-170
9	-8.510302641620927e+133	-7.996921074717953e+128	-1.684379693760117e+129

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	71
1	69	71
2	70	71
3	70	71

end0.0ms

sample878.0ms

Algorithm

intervals

Results

278.0ms	6077×	body	80	valid
187.0ms	692×	body	2560	valid
109.0ms	487×	body	1280	valid
97.0ms	272×	body	5120	valid
42.0ms	248×	body	640	valid
18.0ms	139×	body	320	valid
7.0ms	85×	body	160	valid