Details

sample1.0s

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	195×	body	80	valid
9.0ms	20×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	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: 39.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(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))
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)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (90.0ms)

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

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 19.1b

Counts

64 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(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:

9.0ms	(* (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)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

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

prune131.0ms

Filtered

74 candidates to 136 candidates (-83.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	134	8	142

Merged error: 19.1b

Counts

142 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.9b	(exp (log (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
8.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
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)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify118.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (111.0ms)

Iter	Nodes	Cost
0	193	715
1	489	591
2	1180	550
3	3706	542
4	5002	540

prune137.0ms

Filtered

60 candidates to 70 candidates (-16.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	68	10	78

Merged error: 19.1b

Counts

78 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.8b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
17.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify112.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 4 (104.0ms)

Iter	Nodes	Cost
0	208	622
1	485	555
2	1193	507
3	3624	495
4	5003	493

prune103.0ms

Filtered

62 candidates to 75 candidates (-21.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	75	10	85

Merged error: 19.1b

Counts

85 → 10

regimes299.0ms

Accuracy

59.4% (8.6b remaining)

Error of 25.9b against oracle of 17.3b and baseline of 38.4b

bsearch38.0ms

Steps

Iters	Range		Point
8	6.042511548871019e+93	1.934197131279953e+97	7.043001047710169e+96
9	1.1940696175325994e-252	2.2283784315026441e-246	1.2162908465988943e-252

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

296.0ms	6032×	body	80	valid
190.0ms	675×	body	2560	valid
102.0ms	307×	body	5120	valid
101.0ms	453×	body	1280	valid
63.0ms	318×	body	640	valid
18.0ms	138×	body	320	valid
7.0ms	77×	body	160	valid

Details

sample1.0s

simplify5.0ms

prune3.0ms

localize11.0ms

rewrite23.0ms

series41.0ms

simplify98.0ms

prune115.0ms

localize13.0ms

rewrite41.0ms

series28.0ms

simplify49.0ms

prune131.0ms

localize17.0ms

rewrite41.0ms

series27.0ms

simplify118.0ms

prune137.0ms

localize19.0ms

rewrite34.0ms

series25.0ms

simplify112.0ms

prune103.0ms

regimes299.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling