Details

analyze26.0ms

Algorithm: search

sample20.0ms

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

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: 37.9b

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)
35.3b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite23.0ms

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))
8.0ms	(/ (+ (+ (* 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:

9.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
12.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
28.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (28.0ms)

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

prune148.0ms

Filtered

71 candidates to 90 candidates (-26.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 21.1b

Counts

91 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite51.0ms

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)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
27.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	420	2977
1	1428	2846
2	5001	2796

prune212.0ms

Filtered

108 candidates to 168 candidates (-55.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	168	7	175

Merged error: 21.1b

Counts

175 → 7

localize12.0ms

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))
35.2b	(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:

5.0ms	(+ (+ (* 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)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(+ (* x x) (* y y))
29.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (29.0ms)

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

prune135.0ms

Filtered

72 candidates to 114 candidates (-58.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	111	10	121

Merged error: 21.0b

Counts

121 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod`
130×	`add-sqr-sqrt`
106×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
47×	`cbrt-prod`
43×	`associate-r`
24×	`unswap-sqr`
13×	`associate-l`
10×	`pow1` `sqrt-div`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `div-inv`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
30.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
45.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify125.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	414	3970
1	1331	3861
2	4398	3765
3	5001	3713

prune324.0ms

Filtered

125 candidates to 201 candidates (-60.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	201	10	211

Merged error: 21.0b

Counts

211 → 10

regimes1.0s

Accuracy

62.5% (7.4b remaining)

Error of 25.4b against oracle of 18.0b and baseline of 37.7b

bsearch81.0ms

Steps

Iters	Range		Point
9	9.891564769644244e+79	1.9136622312600887e+85	1.8336961767942577e+85
9	-8.025519654191015e+113	-5.076236393891551e+107	-3.1207763403391707e+112

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

analyze14.0ms

Algorithm: search

sample557.0ms

Algorithm

intervals

Results

387.0ms

8000×

body

valid

Details

analyze26.0ms

sample20.0ms

simplify5.0ms

prune4.0ms

localize9.0ms

rewrite23.0ms

series55.0ms

simplify38.0ms

prune148.0ms

localize14.0ms

rewrite51.0ms

series104.0ms

simplify66.0ms

prune212.0ms

localize12.0ms

rewrite26.0ms

series66.0ms

simplify42.0ms

prune135.0ms

localize16.0ms

rewrite58.0ms

series112.0ms

simplify125.0ms

prune324.0ms

regimes1.0s

bsearch81.0ms

simplify2.0ms

end0.0ms

analyze14.0ms

sample557.0ms

Profiling