Details

sample27.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify5.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.5b

Counts

2 → 1

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	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
27.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (28.0ms)

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

prune154.0ms

Filtered

90 candidates to 71 candidates (21.1%)

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: 18.6b

Counts

91 → 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))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
31.9b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite23.0ms

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:

5.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
7.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series61.0ms

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)))
32.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify45.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (11.0ms)

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

prune97.0ms

Filtered

71 candidates to 50 candidates (29.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	72	5	77

Merged error: 18.6b

Counts

77 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.2b	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
31.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite26.0ms

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:

5.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
10.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
29.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify37.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (30.0ms)

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

prune107.0ms

Filtered

83 candidates to 58 candidates (30.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Merged error: 18.6b

Counts

88 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
31.9b	(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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

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

prune121.0ms

Filtered

114 candidates to 73 candidates (36.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	111	8	119

Merged error: 18.6b

Counts

119 → 8

regimes731.0ms

Accuracy

59.8% (7.9b remaining)

Error of 26.6b against oracle of 18.7b and baseline of 38.4b

bsearch36.0ms

Steps

Iters	Range		Point
8	6.944055718514634e+55	1.987909056376937e+59	1.9652265065732148e+59
8	-2.6907717808382143e+96	-5.954044022157104e+93	-2.6539237641101247e+96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	33	13
2	33	13

end0.0ms

sample679.0ms

Algorithm

intervals

Results

377.0ms

8000×

body

valid

Details

sample27.0ms

simplify5.0ms

prune4.0ms

localize9.0ms

rewrite25.0ms

series58.0ms

simplify36.0ms

prune154.0ms

localize11.0ms

rewrite23.0ms

series61.0ms

simplify45.0ms

prune97.0ms

localize10.0ms

rewrite26.0ms

series63.0ms

simplify37.0ms

prune107.0ms

localize10.0ms

rewrite27.0ms

series68.0ms

simplify46.0ms

prune121.0ms

regimes731.0ms

bsearch36.0ms

simplify2.0ms

end0.0ms

sample679.0ms

Profiling