Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 72.674561%

Results

9.0ms	196×	body	80	valid
6.0ms	22×	body	2560	valid
4.0ms	18×	body	1280	valid
2.0ms	11×	body	640	valid
2.0ms	5×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	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

prune4.0ms

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: 35.2b

Counts

2 → 1

localize12.0ms

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))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
26.5b	(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)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (87.0ms)

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

prune115.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	5	64

Merged error: 16.9b

Counts

64 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.6b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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)))))
14.0ms	(+ (* (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)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(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

prune129.0ms

Filtered

75 candidates to 136 candidates (-81.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Merged error: 16.9b

Counts

141 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
10.1b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

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:

10.0ms	(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)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
7.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	438	1011
1	1505	897
2	5001	864

prune149.0ms

Filtered

66 candidates to 103 candidates (-56.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	103	6	109

Merged error: 16.9b

Counts

109 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(exp (log (+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)))
10.1b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
26.5b	(sqrt (+ (* re re) (* im im)))
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

18.0ms	(exp (log (+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)))
17.0ms	(+ (* (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)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(exp (log (+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)))
7.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	205	849
1	562	709
2	1853	663
3	5001	633

prune140.0ms

Filtered

61 candidates to 70 candidates (-14.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	69	7	76

Merged error: 16.9b

Counts

76 → 7

regimes256.0ms

Accuracy

58.9% (8.7b remaining)

Error of 26.3b against oracle of 17.6b and baseline of 38.7b

bsearch35.0ms

Steps

Iters	Range		Point
8	2.9962523261321446e+144	2.3352747435630826e+147	7.053533511636715e+146
5	2.8157510625046925e-305	7.947899151719585e-305	2.869449096011981e-305

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample2.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 72.674561%

Results

304.0ms	6070×	body	80	valid
191.0ms	657×	body	2560	valid
114.0ms	490×	body	1280	valid
95.0ms	275×	body	5120	valid
54.0ms	304×	body	640	valid
18.0ms	131×	body	320	valid
7.0ms	73×	body	160	valid

Details

sample1.4s

simplify5.0ms

prune4.0ms

localize12.0ms

rewrite22.0ms

series44.0ms

simplify93.0ms

prune115.0ms

localize13.0ms

rewrite41.0ms

series28.0ms

simplify47.0ms

prune129.0ms

localize16.0ms

rewrite37.0ms

series50.0ms

simplify57.0ms

prune149.0ms

localize20.0ms

rewrite44.0ms

series29.0ms

simplify67.0ms

prune140.0ms

regimes256.0ms

bsearch35.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling