Details

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

9.0ms	192×	body	80	valid
7.0ms	26×	body	2560	valid
3.0ms	12×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	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

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: 35.9b

Counts

2 → 1

localize11.0ms

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)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
26.1b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune111.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Merged error: 15.2b

Counts

64 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (+ (* re re) (* im im))) re)
4.8b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
19.6b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
26.1b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

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)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
22.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
14.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	440	1427
1	1601	1331
2	5002	1323

prune181.0ms

Filtered

85 candidates to 132 candidates (-55.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	129	8	137

Merged error: 11.7b

Counts

137 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
26.0b	(sqrt (* 2.0 (pow im 2)))
26.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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:

12.0ms	(/ (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)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (* 2.0 (pow im 2)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	386	1461
1	1401	1391
2	5001	1364

prune192.0ms

Filtered

81 candidates to 116 candidates (-43.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	115	9	124

Merged error: 8.2b

Counts

124 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs im))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
26.1b	(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:

12.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(* (sqrt 2.0) (fabs im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(* (sqrt 2.0) (fabs im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	447	902
1	2073	834
2	5002	825

prune126.0ms

Filtered

68 candidates to 99 candidates (-45.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	98	10	108

Merged error: 6.0b

Counts

108 → 10

regimes622.0ms

Accuracy

64.4% (10.5b remaining)

Error of 18.4b against oracle of 7.9b and baseline of 37.5b

bsearch175.0ms

Steps

Iters	Range		Point
10	5.402763538167712e+37	1.3546762636982592e+48	1.2929770049332553e+48
10	7.434218957269815e-282	1.0117703310727486e-268	1.2857354667385593e-281
7	-9.30865422453791e-251	-4.436929780479901e-252	-4.657708075399103e-252
10	-4.208996924046687e+59	-3.229945642918165e+45	-4.116966419773547e+59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	38
1	62	38

end0.0ms

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

298.0ms	6099×	body	80	valid
186.0ms	683×	body	2560	valid
100.0ms	457×	body	1280	valid
90.0ms	277×	body	5120	valid
48.0ms	264×	body	640	valid
21.0ms	148×	body	320	valid
6.0ms	72×	body	160	valid

Details

sample3.6s

simplify5.0ms

prune3.0ms

localize11.0ms

rewrite23.0ms

series44.0ms

simplify99.0ms

prune111.0ms

localize14.0ms

rewrite39.0ms

series50.0ms

simplify59.0ms

prune181.0ms

localize15.0ms

rewrite32.0ms

series41.0ms

simplify50.0ms

prune192.0ms

localize15.0ms

rewrite29.0ms

series45.0ms

simplify61.0ms

prune126.0ms

regimes622.0ms

bsearch175.0ms

simplify2.0ms

end0.0ms

sample4.6s

Profiling