Details

sample34.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify9.0ms

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: 37.1b

Counts

2 → 1

localize19.0ms

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)
34.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite38.0ms

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:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
6.0ms	(+ (* x x) (* y y))
14.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
10.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series275.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
29.0ms	(+ (* x x) (* y y))
48.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
162.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

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

prune235.0ms

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: 18.3b

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)))
34.5b	(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:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* 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))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
26.0ms	(+ (* x x) (* y y))
53.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
167.0ms	(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

prune147.0ms

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: 18.3b

Counts

77 → 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))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.4b	(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:

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)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
227.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

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

prune220.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 18.2b

Counts

120 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z))))
0.8b	(/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))
34.5b	(sqrt (/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
102×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
50×	`sqrt-prod`
18×	`associate-/r*` `associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`div-inv`
9×	`flip3-+` `flip-+`
8×	`div-exp`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
5×	`rem-sqrt-square`
4×	`cbrt-undiv`
3×	`sqrt-pow1`
2×	`rec-exp` `pow-flip` `frac-2neg` `1-exp` `clear-num` `inv-pow`
1×	`+-commutative` `pow1/2` `sqrt-div` `sum-log`

Counts

4 → 191

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
13.0ms	(/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z))))
6.0ms	(/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))
11.0ms	(sqrt (/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
53.0ms	(/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z))))
52.0ms	(/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))
169.0ms	(sqrt (/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	615	2729
1	2859	2505
2	5001	2293

prune295.0ms

Filtered

203 candidates to 106 candidates (52.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	203	9	212

Merged error: 18.2b

Counts

212 → 9

regimes357.0ms

Accuracy

63% (7.3b remaining)

Error of 25.6b against oracle of 18.3b and baseline of 38.0b

bsearch72.0ms

Steps

Iters	Range		Point
9	1.9303370681519622e+121	1.2392158031794936e+127	2.751642297276684e+123
7	-4.866704026213251e+114	-2.1959671689766027e+112	-4.1883907689960167e+114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	34	13
2	34	13

end0.0ms

sample515.0ms

Algorithm

intervals

Results

352.0ms

8000×

body

valid