Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify7.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 38.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite24.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series274.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* z z))
51.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
162.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

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

prune215.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 18.6b

Counts

91 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(* 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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
7.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* z z))
50.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
331.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify44.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (10.0ms)

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

prune135.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 18.6b

Counts

78 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.2b	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
11.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
38.0ms	(+ (+ (* x x) (* y y)) (* z z))
161.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	286	680
1	1342	648
2	5002	645

prune165.0ms

Filtered

83 candidates to 57 candidates (68.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	6	89

Merged error: 18.6b

Counts

89 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite26.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* z z))
216.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
94.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

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

prune199.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	111	9	120

Merged error: 18.5b

Counts

120 → 9

regimes360.0ms

Accuracy

62.7% (7.4b remaining)

Error of 25.1b against oracle of 17.7b and baseline of 37.5b

bsearch61.0ms

Steps

Iters	Range		Point
10	1.7826190976464906e+97	7.552700620960131e+107	1.3566371815103393e+105
5	-1.7575017886047935e+118	-4.9561533689906815e+117	-1.6174687293654252e+118

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

sample449.0ms

Algorithm

intervals

Results

283.0ms

8000×

body

valid