Details

sample33.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

11.0ms

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: 39.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.7b	(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:

4.0ms	(+ (* 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))

series48.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (112.0ms)

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

prune135.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Merged error: 15.8b

Counts

75 → 6

localize11.0ms

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)))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

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))
16.0ms	(* (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)))
19.0ms	(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

prune116.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Merged error: 15.7b

Counts

90 → 6

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))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite22.0ms

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:

4.0ms	(+ (* 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:

5.0ms	(+ (* x x) (* y y))
30.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify93.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

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

prune123.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 15.6b

Counts

104 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (fabs (/ (cbrt 1) (cbrt 3.0))))
1.0b	(/ (cbrt 1) (cbrt 3.0))
1.0b	(/ (cbrt 1) (cbrt 3.0))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

84×	`cbrt-prod`
72×	`times-frac`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-/r` `associate-/l`
10×	`add-exp-log`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `associate-*l/` `clear-num` `flip-+` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

9.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (fabs (/ (cbrt 1) (cbrt 3.0))))
5.0ms	(/ (cbrt 1) (cbrt 3.0))
5.0ms	(/ (cbrt 1) (cbrt 3.0))
7.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series45.0ms

Counts

4 → 8

Calls

4 calls:

26.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (fabs (/ (cbrt 1) (cbrt 3.0))))
0.0ms	(/ (cbrt 1) (cbrt 3.0))
0.0ms	(/ (cbrt 1) (cbrt 3.0))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify99.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	269	1435
1	833	1386
2	3373	1353
3	5001	1017

prune238.0ms

Filtered

81 candidates to 167 candidates (-106.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	164	12	176

Merged error: 15.6b

Counts

176 → 12

regimes937.0ms

Accuracy

59.9% (7.9b remaining)

Error of 26.1b against oracle of 18.2b and baseline of 38.0b

bsearch73.0ms

Steps

Iters	Range		Point
9	1.2011116939796816e+51	8.164803710251398e+58	8.037198245725728e+58
10	-1.2572007808754726e+58	-7.692543456597435e+47	-1.2459053091720248e+58

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

sample562.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

387.0ms

8000×

body

valid

Details

sample33.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series48.0ms

simplify121.0ms

prune135.0ms

localize11.0ms

rewrite27.0ms

series52.0ms

simplify117.0ms

prune116.0ms

localize10.0ms

rewrite22.0ms

series55.0ms

simplify93.0ms

prune123.0ms

localize16.0ms

rewrite31.0ms

series45.0ms

simplify99.0ms

prune238.0ms

regimes937.0ms

bsearch73.0ms

simplify2.0ms

end0.0ms

sample562.0ms

Profiling