Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 38.3b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

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

series252.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (+ (* x x) (* y y)) (* z z))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
163.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	259	758
1	1001	695
2	4255	689
3	5001	687

prune323.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Merged error: 19.7b

Counts

77 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.7b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

5.0ms	(+ (+ (* 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))))

series246.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
52.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
159.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify40.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	244	469
1	1256	426
2	5002	424

prune189.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 19.7b

Counts

63 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

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

series318.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (+ (* x x) (* y y)) (* z z))
163.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify117.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	220	610
1	992	582
2	4454	575
3	5001	575

prune226.0ms

Filtered

69 candidates to 46 candidates (66.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 19.7b

Counts

75 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

5.0ms	(+ (+ (* 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)))

series368.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
234.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify113.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	264	1246
1	989	1175
2	4693	1148
3	5002	1148

prune286.0ms

Filtered

100 candidates to 62 candidates (62.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	97	10	107

Merged error: 19.6b

Counts

107 → 10

regimes883.0ms

Accuracy

62.3% (7.5b remaining)

Error of 25.1b against oracle of 17.6b and baseline of 37.6b

bsearch96.0ms

Steps

Iters	Range		Point
8	8.124947580121196e+141	2.3710053120370955e+144	1.2546636830809128e+144
11	-3.234739137796827e+160	-1.1042016886584325e+130	-3.0315072087379574e+131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	33	12
2	33	12

end0.0ms

sample632.0ms

Algorithm

intervals

Results

347.0ms

8000×

body

valid

Details

sample26.0ms

simplify8.0ms

prune4.0ms

localize14.0ms

rewrite22.0ms

series252.0ms

simplify115.0ms

prune323.0ms

localize9.0ms

rewrite19.0ms

series246.0ms

simplify40.0ms

prune189.0ms

localize10.0ms

rewrite21.0ms

series318.0ms

simplify117.0ms

prune226.0ms

localize11.0ms

rewrite22.0ms

series368.0ms

simplify113.0ms

prune286.0ms

regimes883.0ms

bsearch96.0ms

simplify2.0ms

end0.0ms

sample632.0ms

Profiling