Details

sample50.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.996948%

Results

26.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune6.0ms

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: 31.0b

Counts

2 → 1

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

6.0ms	(+ (* re re) (* im im))
12.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

series32.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
19.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	259	745
1	894	701
2	2872	696
3	5001	694

prune164.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 6.5b

Counts

84 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.5b	(/ (log 10.0) (log (+ (* re re) (* im im))))
29.7b	(log (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
47×	`pow1`
43×	`log-pow`
24×	`associate-/r*`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`log-prod`
2×	`log-div` `frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `rem-log-exp` `sum-log` `associate-/r/`

Counts

4 → 159

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
4.0ms	(log (+ (* re re) (* im im)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
21.0ms	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
25.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	490	1926
1	2126	1824
2	5002	1813

prune303.0ms

Filtered

111 candidates to 171 candidates (-54.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	164	7	171
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	175	10	185

Merged error: 6.4b

Counts

185 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
0.4b	(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
0.4b	(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
29.7b	(log (+ (* re re) (* im im)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

896×	`times-frac`
537×	`add-sqr-sqrt`
521×	`sqrt-prod`
389×	`add-cube-cbrt` `*-un-lft-identity`
197×	`associate-r`
169×	`pow1`
163×	`log-pow`
46×	`associate-l`
36×	`associate-/r*`
35×	`unswap-sqr`
33×	`add-exp-log`
32×	`add-cbrt-cube`
17×	`div-inv`
13×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`log-prod`
2×	`log-div` `frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 612

Calls

4 calls:

153.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
12.0ms	(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
4.0ms	(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
3.0ms	(log (+ (* re re) (* im im)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))))
26.0ms	(/ (sqrt 1/2) (/ (sqrt (log 10.0)) (log (+ (* re re) (* im im)))))
29.0ms	(/ (sqrt (log 10.0)) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify122.0ms

Algorithm

egg-herbie

Counts

624 → 624

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1438	10601
1	5001	9984

prune1.2s

Filtered

248 candidates to 624 candidates (-151.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	618	6	624
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	621	13	634

Merged error: 6.3b

Counts

634 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.5b	(* (sqrt 1/2) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
0.5b	(/ (log 10.0) (log (+ (* re re) (* im im))))
29.7b	(log (+ (* re re) (* im im)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

476×	`times-frac`
249×	`add-sqr-sqrt`
217×	`add-cube-cbrt` `*-un-lft-identity`
135×	`sqrt-prod`
125×	`associate-r`
121×	`pow1`
115×	`log-pow`
24×	`associate-/r*`
21×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`div-inv`
10×	`associate-/l*` `unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l`
4×	`add-log-exp`
3×	`log-prod` `prod-exp` `cbrt-unprod`
2×	`log-div` `frac-2neg` `clear-num` `associate-/r/`
1×	`flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `-commutative` `flip-+`

Counts

4 → 368

Calls

4 calls:

9.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
35.0ms	(* (sqrt 1/2) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
3.0ms	(log (+ (* re re) (* im im)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
26.0ms	(* (sqrt 1/2) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
25.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify128.0ms

Algorithm

egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	841	4988
1	4046	4674
2	5001	4659

prune495.0ms

Filtered

183 candidates to 380 candidates (-107.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	376	4	380
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	378	15	393

Merged error: 6.3b

Counts

393 → 15

regimes714.0ms

Accuracy

57.5% (10.6b remaining)

Error of 17.9b against oracle of 7.3b and baseline of 32.2b

bsearch109.0ms

Steps

Iters	Range		Point
3	1.5832715914527118e+84	2.187712400463558e+84	2.0069927548790835e+84
8	1.1862939267725684e-191	3.416246219259482e-189	1.0744771963851055e-190
9	-2.207489823042089e-242	-9.853989006496261e-251	-2.641698775493714e-245
8	-4.3855662648781583e+110	-1.5585363657692155e+106	-1.659310464645964e+110

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	65
1	66	65

end0.0ms

sample716.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.996948%

Results

503.0ms

8000×

body

valid

Details

sample50.0ms

simplify5.0ms

prune6.0ms

localize20.0ms

rewrite30.0ms

series32.0ms

simplify93.0ms

prune164.0ms

localize14.0ms

rewrite25.0ms

series64.0ms

simplify66.0ms

prune303.0ms

localize15.0ms

rewrite222.0ms

series95.0ms

simplify122.0ms

prune1.2s

localize15.0ms

rewrite76.0ms

series86.0ms

simplify128.0ms

prune495.0ms

regimes714.0ms

bsearch109.0ms

simplify2.0ms

end0.0ms

sample716.0ms

Profiling