Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	168×	body	80	valid
7.0ms	27×	body	2560	valid
4.0ms	20×	body	1280	valid
4.0ms	13×	body	5120	valid
3.0ms	19×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 45.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
33.9b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (* re re) (* im im))
10.0ms	(+ (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

prune121.0ms

Filtered

63 candidates to 52 candidates (17.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	6	64

Merged error: 24.9b

Counts

64 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (sqrt (+ (* re re) (* im im))) re)
6.2b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
25.8b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
33.9b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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)
13.0ms	(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)))

series47.0ms

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))))
11.0ms	(/ (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 (44.0ms)

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

prune191.0ms

Filtered

132 candidates to 85 candidates (35.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	131	7	138

Merged error: 20.4b

Counts

138 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
0.1b	(- (sqrt (+ (* re re) (* im im))) re)
6.2b	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
33.9b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
17×	`sqrt-prod`
13×	`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×	`pow1/2`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `flip3-+` `diff-log` `associate-*r/` `pow-prod-down` `clear-num` `associate-/r/` `flip--` `flip-+`

Counts

4 → 148

Calls

4 calls:

11.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
25.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	643	1958
1	3082	1844
2	5002	1831

prune179.0ms

Filtered

160 candidates to 105 candidates (34.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	159	8	167

Merged error: 16.7b

Counts

167 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (sqrt (+ (* re re) (* im im))) re)
0.2b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
32.3b	(sqrt (* 2.0 (pow im 2)))
33.9b	(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:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(/ (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)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
22.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (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 (36.0ms)

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

prune170.0ms

Filtered

116 candidates to 81 candidates (30.2%)

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: 13.0b

Counts

124 → 9

regimes168.0ms

Accuracy

53.2% (11.5b remaining)

Error of 23.0b against oracle of 11.4b and baseline of 36.1b

bsearch104.0ms

Steps

Iters	Range		Point
10	160641522886.7463	8.565987169494656e+25	170494105449.52274
7	1.3770814234996415e-63	2.135859847469984e-61	4.6543446158022345e-63
7	7.385488744925596e-118	7.805537377269367e-116	1.544391144474447e-116
10	-1.9731800516709207e+159	-1.4515475039626118e+147	-1.3278651885174792e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	35
1	56	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

275.0ms	5471×	body	80	valid
263.0ms	958×	body	2560	valid
142.0ms	413×	body	5120	valid
134.0ms	595×	body	1280	valid
56.0ms	317×	body	640	valid
22.0ms	165×	body	320	valid
7.0ms	81×	body	160	valid

Details

sample43.0ms

simplify6.0ms

prune3.0ms

localize11.0ms

rewrite22.0ms

series45.0ms

simplify99.0ms

prune121.0ms

localize14.0ms

rewrite42.0ms

series47.0ms

simplify59.0ms

prune191.0ms

localize13.0ms

rewrite41.0ms

series49.0ms

simplify88.0ms

prune179.0ms

localize15.0ms

rewrite32.0ms

series39.0ms

simplify50.0ms

prune170.0ms

regimes168.0ms

bsearch104.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling