Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 82.397461%

Results

13.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

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: 36.7b

Counts

2 → 1

localize194.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series44.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify118.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4391	642
3	5001	640

prune133.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	5	75

Merged error: 18.9b

Counts

75 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
14.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series52.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
28.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify117.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	318	858
1	1226	828
2	4716	804
3	5001	796

prune113.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 18.9b

Counts

89 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `sqrt-div`
3×	`flip3-+` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 89

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series55.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (* x x) (* y y))
29.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	294	1188
1	1083	1124
2	4069	1101
3	5002	1101

prune125.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	95	8	103

Merged error: 18.8b

Counts

103 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

5.0ms

(* x (sqrt 0.3333333333333333))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(* x (sqrt 0.3333333333333333))

simplify60.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	69	84
1	245	80
2	569	78
3	893	78
4	2001	78
5	5001	78

prune28.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	21	12	33

Merged error: 18.8b

Counts

33 → 12

regimes975.0ms

Accuracy

62.5% (7.3b remaining)

Error of 26.2b against oracle of 18.9b and baseline of 38.4b

bsearch32.0ms

Steps

Iters	Range		Point
3	2.0383219502338506e+106	2.661912141880486e+106	2.622937754902571e+106
9	-2.5404446163119167e+63	-1.7340395696170638e+55	-2.4968492265159954e+63

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	14
1	37	14
2	37	14

end0.0ms

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 82.397461%

Results

400.0ms

8000×

body

valid

Details

sample1.4s

simplify5.0ms

prune4.0ms

localize194.0ms

rewrite19.0ms

series44.0ms

simplify118.0ms

prune133.0ms

localize12.0ms

rewrite25.0ms

series52.0ms

simplify117.0ms

prune113.0ms

localize10.0ms

rewrite20.0ms

series55.0ms

simplify96.0ms

prune125.0ms

localize3.0ms

rewrite5.0ms

series4.0ms

simplify60.0ms

prune28.0ms

regimes975.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling