Details

sample25.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

12.0ms

256×

body

valid

simplify6.0ms

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

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: 37.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite20.0ms

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:

4.0ms	(+ (* x x) (* y y))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series49.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
16.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
27.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (111.0ms)

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

prune138.0ms

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: 16.3b

Counts

75 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite26.0ms

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)))

series55.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
27.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
22.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify118.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (109.0ms)

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

prune115.0ms

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: 16.3b

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))
34.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite21.0ms

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)))

series57.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
33.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify98.0ms

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

prune127.0ms

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: 16.2b

Counts

103 → 8

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite6.0ms

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))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(* x (sqrt 0.3333333333333333))

simplify60.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (9.0ms)

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

prune30.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	22	11	33

Merged error: 16.2b

Counts

33 → 11

regimes847.0ms

Accuracy

63.1% (7.2b remaining)

Error of 25.6b against oracle of 18.4b and baseline of 37.9b

bsearch41.0ms

Steps

Iters	Range		Point
9	5.83254265182303e+139	1.4092267891425916e+149	5.8246996730762875e+144
7	-1.728787615673916e+92	-1.634529202392062e+90	-1.2253025585842285e+92

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	39	14
2	39	14

end0.0ms

sample645.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

387.0ms

8000×

body

valid

Details

sample25.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite20.0ms

series49.0ms

simplify119.0ms

prune138.0ms

localize13.0ms

rewrite26.0ms

series55.0ms

simplify118.0ms

prune115.0ms

localize10.0ms

rewrite21.0ms

series57.0ms

simplify98.0ms

prune127.0ms

localize4.0ms

rewrite6.0ms

series5.0ms

simplify60.0ms

prune30.0ms

regimes847.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

sample645.0ms

Profiling