Details

analyze18.0ms

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 99.975586%

sample21.0ms

Algorithm

intervals

Results

11.0ms

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

prune3.0ms

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: 36.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.5b	(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)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series47.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
15.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
27.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (113.0ms)

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

prune135.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

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: 19.7b

Counts

75 → 7

localize11.0ms

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))))
33.5b	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite37.0ms

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))
16.0ms	(* 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)))))

series45.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (pow y 2) (pow z 2))
13.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
27.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (33.0ms)

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

prune126.0ms

Filtered

38 candidates to 60 candidates (-57.9%)

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: 19.7b

Counts

67 → 7

localize16.0ms

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)))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.4b	(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:

7.0ms	(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)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(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)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
22.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify65.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (38.0ms)

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

prune216.0ms

Filtered

109 candidates to 168 candidates (-54.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	167	8	175

Merged error: 19.7b

Counts

175 → 8

localize15.0ms

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))))
33.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.4b	(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))
47.0ms	(* (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)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify107.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	449	5736
1	2178	5405
2	5002	5370

prune342.0ms

Filtered

149 candidates to 328 candidates (-120.1%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	325	3	328
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	325	11	336

Merged error: 19.6b

Counts

336 → 11

Details

analyze18.0ms

sample21.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series47.0ms

simplify121.0ms

prune135.0ms

localize11.0ms

rewrite37.0ms

series45.0ms

simplify40.0ms

prune126.0ms

localize16.0ms

rewrite51.0ms

series109.0ms

simplify65.0ms

prune216.0ms

localize15.0ms

rewrite91.0ms

series103.0ms

simplify107.0ms

prune342.0ms

regimes966.0ms

bsearch1.0ms

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