Details

sample22.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify6.0ms

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

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: 35.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 65

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series232.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* x x) (* y y))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
157.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4391	642
3	5001	640

prune187.0ms

Filtered

74 candidates to 60 candidates (81.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 17.2b

Counts

75 → 7

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow y 2) (pow z 2))
0.1b	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
33.4b	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
8×	`pow1`
7×	`add-sqr-sqrt` `distribute-lft-out`
6×	`associate-r`
5×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`associate-*r/`
3×	`flip3-+` `associate-l` `flip-+`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sum-log` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

7.0ms	(+ (pow y 2) (pow z 2))
14.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
12.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series236.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (pow y 2) (pow z 2))
47.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
159.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	260	411
1	1384	379
2	5002	378

prune135.0ms

Filtered

60 candidates to 38 candidates (63.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	60	7	67

Merged error: 17.2b

Counts

67 → 7

localize15.0ms

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)))
33.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite55.0ms

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:

7.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
30.0ms	(* (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)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
164.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (41.0ms)

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

prune395.0ms

Filtered

168 candidates to 108 candidates (64.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	168	7	175

Merged error: 17.2b

Counts

175 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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))))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
33.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite65.0ms

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:

32.0ms	(* (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))))
13.0ms	(/ (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)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (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))))
222.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify123.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	414	3970
1	1331	3861
2	4399	3765
3	5001	3713

prune515.0ms

Filtered

201 candidates to 125 candidates (62.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	201	7	208

Merged error: 17.2b

Counts

208 → 7

regimes455.0ms

Accuracy

63.1% (7.4b remaining)

Error of 25.7b against oracle of 18.3b and baseline of 38.3b

bsearch73.0ms

Steps

Iters	Range		Point
6	1.8962655321734537e+99	2.2447661859045347e+100	2.196251001109748e+100
9	-5.837703290195856e+113	-6.047772196803219e+108	-5.78777483018727e+113

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

sample585.0ms

Algorithm

intervals

Results

405.0ms

8000×

body

valid

Details

sample22.0ms

simplify6.0ms

prune2.0ms

localize10.0ms

rewrite19.0ms

series232.0ms

simplify119.0ms

prune187.0ms

localize15.0ms

rewrite35.0ms

series236.0ms

simplify38.0ms

prune135.0ms

localize15.0ms

rewrite55.0ms

series514.0ms

simplify66.0ms

prune395.0ms

localize18.0ms

rewrite65.0ms

series743.0ms

simplify123.0ms

prune515.0ms

regimes455.0ms

bsearch73.0ms

simplify2.0ms

end0.0ms

sample585.0ms

Profiling