Details

sample84.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.975586%

Results

13.0ms

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

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: 38.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
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))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune348.0ms

Filtered

71 candidates to 90 candidates (-26.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 16.9b

Counts

91 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.4b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3-+` `associate-*r/` `sum-log` `flip-+`
3×	`associate-r` `associate-l`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
8.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
13.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
28.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify45.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	310	539
1	1615	492
2	5001	492

prune95.0ms

Filtered

50 candidates to 71 candidates (-42.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 16.9b

Counts

77 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
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)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
32.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	330	1316
1	1338	1241
2	5002	1218

prune143.0ms

Filtered

73 candidates to 114 candidates (-56.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	110	10	120

Merged error: 16.8b

Counts

120 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-prod`
42×	`add-sqr-sqrt`
39×	`times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
16×	`cbrt-prod`
7×	`pow1`
6×	`rem-sqrt-square`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`cbrt-div` `pow1/3`

Counts

4 → 100

Calls

4 calls:

6.0ms	(cbrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
7.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series132.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))
28.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
26.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
26.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	220	1326
1	506	1239
2	1829	1229
3	5001	1215

prune273.0ms

Filtered

95 candidates to 112 candidates (-17.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	112	10	122

Merged error: 16.8b

Counts

122 → 10

regimes884.0ms

Accuracy

62.1% (7.4b remaining)

Error of 25.7b against oracle of 18.3b and baseline of 37.8b

bsearch86.0ms

Steps

Iters	Range		Point
8	1.681660906044602e+98	9.281075812664692e+100	9.156732467259482e+100
9	-5.0950487023111706e+88	-1.2226750841628108e+81	-5.016372774839576e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	32	12
2	32	12

end0.0ms

sample703.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.975586%

Results

394.0ms

8000×

body

valid

Details

sample84.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite28.0ms

series54.0ms

simplify40.0ms

prune348.0ms

localize9.0ms

rewrite24.0ms

series56.0ms

simplify45.0ms

prune95.0ms

localize11.0ms

rewrite27.0ms

series66.0ms

simplify47.0ms

prune143.0ms

localize15.0ms

rewrite28.0ms

series132.0ms

simplify69.0ms

prune273.0ms

regimes884.0ms

bsearch86.0ms

simplify2.0ms

end0.0ms

sample703.0ms

Profiling