Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify7.0ms

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

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: 38.9b

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)
36.2b	(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:

5.0ms	(+ (+ (* 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))

series271.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
25.0ms	(+ (* x x) (* y y))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
159.0ms	(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

prune219.0ms

Filtered

90 candidates to 71 candidates (78.9%)

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: 20.1b

Counts

91 → 6

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	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
36.3b	(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:

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

series272.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (+ (* x x) (* y y)) (* z z))
31.0ms	(+ (* x x) (* y y))
47.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
160.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify41.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (9.0ms)

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

prune154.0ms

Filtered

71 candidates to 50 candidates (70.4%)

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: 20.1b

Counts

77 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
122×	`add-sqr-sqrt`
84×	`times-frac`
55×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
11×	`pow1`
9×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

6.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
24.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
179.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
95.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify64.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	391	2965
1	1318	2831
2	5002	2779

prune398.0ms

Filtered

168 candidates to 108 candidates (64.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	168	6	174

Merged error: 20.1b

Counts

174 → 6

localize21.0ms

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))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite32.0ms

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:

5.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
11.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
8.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (+ (* x x) (* y y)) (* z z))
25.0ms	(+ (* x x) (* y y))
219.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
95.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (30.0ms)

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

prune212.0ms

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: 20.0b

Counts

120 → 9

regimes407.0ms

Accuracy

61% (7.8b remaining)

Error of 26.4b against oracle of 18.6b and baseline of 38.6b

bsearch62.0ms

Steps

Iters	Range		Point
8	8.889439910526904e+123	3.5273752339794244e+127	2.3647953557231046e+127
7	-2.2268984505389627e+51	-5.086139815324964e+49	-2.1953272704890833e+51

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

sample466.0ms

Algorithm

intervals

Results

290.0ms

8000×

body

valid

Details

sample18.0ms

simplify7.0ms

prune2.0ms

localize9.0ms

rewrite24.0ms

series271.0ms

simplify40.0ms

prune219.0ms

localize10.0ms

rewrite24.0ms

series272.0ms

simplify41.0ms

prune154.0ms

localize18.0ms

rewrite48.0ms

series523.0ms

simplify64.0ms

prune398.0ms

localize21.0ms

rewrite32.0ms

series374.0ms

simplify47.0ms

prune212.0ms

regimes407.0ms

bsearch62.0ms

simplify2.0ms

end0.0ms

sample466.0ms

Profiling