Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	181×	body	80	valid
6.0ms	29×	body	2560	valid
3.0ms	14×	body	5120	valid
3.0ms	18×	body	1280	valid
1.0ms	10×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	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: 43.6b

Counts

2 → 1

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)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
179.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune172.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 20.2b

Counts

64 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (+ (* re re) (* im im))) re)
7.9b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
20.6b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
21×	`unpow-prod-down`
20×	`difference-of-squares`
14×	`sqrt-prod`
10×	`distribute-lft-out--`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
7×	`unpow2` `sqr-pow`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `sqrt-div` `div-exp`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 120

Calls

4 calls:

7.0ms	(- (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)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
197.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
74.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	447	1428
1	1582	1323
2	5001	1313

prune325.0ms

Filtered

132 candidates to 85 candidates (64.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Merged error: 16.5b

Counts

138 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (* 2.0 (pow im 2)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`sqrt-div` `associate-/l*`
2×	`flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (* 2.0 (pow im 2)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (* 2.0 (pow im 2)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	393	1462
1	1376	1383
2	5001	1354

prune307.0ms

Filtered

116 candidates to 81 candidates (69.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Merged error: 10.8b

Counts

123 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.4b	(* (sqrt 2.0) (fabs im))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac` `associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`sqrt-div`
3×	`associate-r` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 87

Calls

4 calls:

11.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
5.0ms	(* (sqrt 2.0) (fabs im))
4.0ms	(sqrt (+ (* re re) (* im im)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
52.0ms	(- (sqrt (+ (* re re) (* im im))) re)
31.0ms	(* (sqrt 2.0) (fabs im))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	450	903
1	1991	826
2	5002	817

prune245.0ms

Filtered

99 candidates to 68 candidates (68.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	96	11	107

Merged error: 8.8b

Counts

107 → 11

regimes130.0ms

Accuracy

49.2% (15.2b remaining)

Error of 22.7b against oracle of 7.5b and baseline of 37.4b

bsearch164.0ms

Steps

Iters	Range	Point
8	3.3685160830587113e-93	1.1118131948146322e-89	4.910461826111689e-93
10	-3.744556309116812e-103	-1.0905044694663493e-116	-1.1044329890532487e-116
10	-8.777387788220042e+125	-4.2027485674795273e+114	-8.15615961666859e+125

Iters

Range

Point

3.3685160830587113e-93

1.1118131948146322e-89

4.910461826111689e-93

-3.744556309116812e-103

-1.0905044694663493e-116

-1.1044329890532487e-116

-8.777387788220042e+125

-4.2027485674795273e+114

-8.15615961666859e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	27
1	52	27

end0.0ms

sample677.0ms

Algorithm

intervals

Results

199.0ms	5987×	body	80	valid
137.0ms	690×	body	2560	valid
78.0ms	500×	body	1280	valid
75.0ms	295×	body	5120	valid
36.0ms	292×	body	640	valid
14.0ms	153×	body	320	valid
5.0ms	83×	body	160	valid