Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
5.0ms	19×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	4×	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

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: 40.7b

Counts

2 → 1

localize10.0ms

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

rewrite27.0ms

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))
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)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
178.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (84.0ms)

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

prune174.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Merged error: 18.0b

Counts

64 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.5b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
23.0b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
48×	`times-frac`
46×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`unpow-prod-down`
18×	`difference-of-squares`
13×	`sqrt-prod`
9×	`add-exp-log` `distribute-lft-out--`
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` `+-commutative` `pow-to-exp` `rem-sqrt-square` `flip3--` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

4 → 116

Calls

4 calls:

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

series333.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
193.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
73.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	456	1373
1	1707	1269
2	5003	1261

prune288.0ms

Filtered

128 candidates to 82 candidates (64.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Merged error: 14.5b

Counts

136 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
5.5b	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
117×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
68×	`add-cube-cbrt`
24×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
12×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
3×	`cbrt-undiv` `sqrt-pow1` `sqrt-div` `div-exp` `associate-/l*`
2×	`flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `sum-log` `associate-/r/`

Counts

4 → 144

Calls

4 calls:

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

series337.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
75.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
195.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	644	1908
1	3122	1783
2	5002	1772

prune336.0ms

Filtered

156 candidates to 103 candidates (66.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	156	8	164

Merged error: 12.8b

Counts

164 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
28.7b	(sqrt (* 2.0 (pow im 2)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

49×	`sqrt-prod`
46×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
10×	`difference-of-squares`
9×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out--`
4×	`sqrt-div` `associate-/l*`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

4 → 100

Calls

4 calls:

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

series299.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
197.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
39.0ms	(sqrt (* 2.0 (pow im 2)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	398	1408
1	1481	1330
2	5002	1304

prune277.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	112	8	120

Merged error: 9.1b

Counts

120 → 8

regimes118.0ms

Accuracy

48.9% (14.3b remaining)

Error of 22.6b against oracle of 8.3b and baseline of 36.3b

bsearch176.0ms

Steps

Iters	Range		Point
9	1.797583913273012e-26	4.624596296664411e-20	3.2163374571899126e-26
3	2.828001728767348e-94	3.9711305604987253e-94	3.185229488683403e-94
7	1.571440827181474e-290	7.523154984281335e-289	7.253421839627516e-289
9	-1.6803274199859986e+155	-1.3968704931933265e+149	-1.3380130268941683e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	42
1	66	42

end0.0ms

sample894.0ms

Algorithm

intervals

Results

276.0ms	5986×	body	80	valid
189.0ms	687×	body	2560	valid
107.0ms	489×	body	1280	valid
100.0ms	301×	body	5120	valid
52.0ms	291×	body	640	valid
21.0ms	162×	body	320	valid
7.0ms	84×	body	160	valid