Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	11	14
1	16	13
2	26	12
3	30	12
done	30	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

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)
37.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `sum-log` `log1p-expm1-u`
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 → 90

Calls

4 calls:

13.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
29.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series287.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
34.0ms	(+ (* x x) (* y y))
50.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.1s

Counts

102 → 102

Iterations

Useful iterations: 3 (827.0ms)

Iter	Nodes	Cost
0	147	1805
1	344	1579
2	1149	1360
3	4538	1348
done	5000	1348

prune309.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.1b

localize11.0ms

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))
37.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sum-log` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 115

Calls

4 calls:

13.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
23.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
16.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
26.0ms	(+ (* x x) (* y y))
222.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.7s

Counts

127 → 127

Iterations

Useful iterations: 3 (554.0ms)

Iter	Nodes	Cost
0	160	2622
1	347	2234
2	1070	2023
3	4039	1987
done	5000	1987

prune354.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
33.8b	(sqrt (+ (* x x) (* y y)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `hypot-udef` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 74

Calls

3 calls:

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

series350.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
284.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.3s

Counts

83 → 83

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	125	1386
1	248	902
2	711	821
3	2335	815
done	5000	815

prune273.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (hypot (hypot x y) z) (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` `expm1-log1p-u` `sqrt-undiv` `hypot-udef` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 42

Calls

1 calls:

3.0ms

(/ (hypot (hypot x y) z) (sqrt 3.0))

series311.0ms

Counts

1 → 3

Calls

1 calls:

311.0ms

(/ (hypot (hypot x y) z) (sqrt 3.0))

simplify4.2s

Counts

45 → 45

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	80	648
1	123	617
2	228	585
3	472	583
4	872	583
5	1155	583
6	1974	583
done	5000	583

prune123.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	11	11
1	14	9
done	14	9

end0.0ms

sample442.0ms

Algorithm

intervals

Results

275.0ms

8000×

body

valid