Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	208×	body	80	valid
4.0ms	14×	body	5120	valid
4.0ms	14×	body	2560	valid
3.0ms	12×	body	1280	valid
0.0ms	3×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	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: 35.9b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune145.0ms

Filtered

49 candidates to 42 candidates (85.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 14.5b

Counts

50 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
20.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
45.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
42.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune264.0ms

Filtered

136 candidates to 74 candidates (54.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 14.5b

Counts

143 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
8.5b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
16.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
52.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	394	992
1	1342	878
2	5001	845

prune313.0ms

Filtered

103 candidates to 66 candidates (64.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	102	8	110

Merged error: 14.5b

Counts

110 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
3.3b	(+ (* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

55×	`sqrt-prod`
43×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
10×	`sqrt-div` `associate-l`
9×	`add-exp-log`
7×	`pow1`
6×	`add-cbrt-cube` `add-log-exp`
5×	`sqrt-pow1` `sqr-pow`
4×	`flip3-+` `flip-+`
3×	`pow1/2` `prod-exp`
2×	`rem-sqrt-square` `associate-*r/` `pow-prod-up`
1×	`+-commutative` `pow-to-exp` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

16.0ms	(* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
13.0ms	(+ (* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
52.0ms	(+ (* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify132.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	276	1353
1	876	1309
2	4525	1293
3	5002	1293

prune283.0ms

Filtered

107 candidates to 71 candidates (66.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	107	8	115

Merged error: 14.5b

Counts

115 → 8

regimes199.0ms

Accuracy

54.2% (9.6b remaining)

Error of 27.4b against oracle of 17.8b and baseline of 38.8b

bsearch106.0ms

Steps

Iters	Range	Point
8	2.1558392991063154e+98	3.0943356273139873e+102	9.121519472730704e+101
9	-1.0921927090926265e-299	-4.707778381284133e-306	-1.4898746708619831e-300
4	-5.350978981580884e-165	-2.701583151381948e-165	-2.768600938278902e-165

Iters

Range

Point

2.1558392991063154e+98

3.0943356273139873e+102

9.121519472730704e+101

-1.0921927090926265e-299

-4.707778381284133e-306

-1.4898746708619831e-300

-5.350978981580884e-165

-2.701583151381948e-165

-2.768600938278902e-165

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	33
1	47	33

end0.0ms

sample857.0ms

Algorithm

intervals

Results

282.0ms	6071×	body	80	valid
179.0ms	686×	body	2560	valid
103.0ms	475×	body	1280	valid
84.0ms	265×	body	5120	valid
46.0ms	273×	body	640	valid
20.0ms	152×	body	320	valid
8.0ms	78×	body	160	valid