Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

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: 39.7b

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))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite28.0ms

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* 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))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (30.0ms)

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

prune395.0ms

Filtered

90 candidates to 71 candidates (21.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	6	91

Merged error: 20.9b

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))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.7b	(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))
3.0ms	(+ (* 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)))

series67.0ms

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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (30.0ms)

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

prune365.0ms

Filtered

114 candidates to 71 candidates (37.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	112	8	120

Merged error: 20.8b

Counts

120 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
0.5b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
36.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

574×	`sqrt-prod`
344×	`add-sqr-sqrt`
284×	`times-frac`
154×	`add-cube-cbrt` `*-un-lft-identity`
73×	`swap-sqr`
43×	`associate-r` `associate-l`
36×	`unswap-sqr`
21×	`pow1`
10×	`sqrt-pow1` `pow1/2` `sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow-prod-up` `div-inv`
4×	`add-log-exp`
3×	`flip3-+` `pow-prod-down` `pow-sqr` `flip-+`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 316

Calls

4 calls:

9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
50.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
31.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
25.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify99.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	449	5730
1	2053	5405
2	5002	5370

prune1.0s

Filtered

328 candidates to 147 candidates (55.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	328	8	336

Merged error: 20.8b

Counts

336 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ x (sqrt 3.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
6×	`associate-/r*`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

4.0ms

(/ x (sqrt 3.0))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(/ x (sqrt 3.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 4 (44.0ms)

Iter	Nodes	Cost
0	103	217
1	273	207
2	715	197
3	2013	197
4	5002	196

prune56.0ms

Filtered

42 candidates to 26 candidates (38.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	36	6	42
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	36	14	50

Merged error: 20.8b

Counts

50 → 14

regimes1.1s

Accuracy

62.1% (7.5b remaining)

Error of 25.9b against oracle of 18.4b and baseline of 38.3b

bsearch98.0ms

Steps

Iters	Range		Point
8	9.555849306330013e+86	1.704051699546871e+90	2.5006745594136055e+89
10	-6.856527875648579e+102	-1.7166838907982538e+84	-6.181068723284219e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	12
1	35	12
2	35	12

end0.0ms

sample597.0ms

Algorithm

intervals

Results

327.0ms

8000×

body

valid

Details

sample24.0ms

simplify5.0ms

prune4.0ms

localize9.0ms

rewrite28.0ms

series55.0ms

simplify39.0ms

prune395.0ms

localize10.0ms

rewrite26.0ms

series67.0ms

simplify43.0ms

prune365.0ms

localize13.0ms

rewrite91.0ms

series106.0ms

simplify99.0ms

prune1.0s

localize3.0ms

rewrite5.0ms

series5.0ms

simplify48.0ms

prune56.0ms

regimes1.1s

bsearch98.0ms

simplify2.0ms

end0.0ms

sample597.0ms

Profiling