Details

sample31.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	22	14
3	24	14
done	24	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite511.0ms

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:

15.0ms	(+ (* x x) (* y y))
454.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series414.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* x x) (* y y))
85.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
292.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: 3 (666.0ms)

Iter	Nodes	Cost
0	128	1436
1	291	1370
2	855	1241
3	2763	1233
done	5001	1233

prune287.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.7b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

15.0ms	(+ (* x x) (* y y))
102.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
49.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series451.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
276.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
143.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.9s

Counts

84 → 84

Iterations

Useful iterations: 3 (713.0ms)

Iter	Nodes	Cost
0	140	1688
1	315	1536
2	794	1451
3	2239	1429
done	5000	1429

prune356.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
32.6b	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
32.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

49×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
9×	`sqrt-div`
8×	`sqrt-pow1`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow1/2` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `frac-2neg` `pow-plus` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 112

Calls

4 calls:

74.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
55.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
49.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
52.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
268.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
146.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
142.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.9s

Counts

124 → 124

Iterations

Useful iterations: 3 (441.0ms)

Iter	Nodes	Cost
0	138	2888
1	236	2399
2	534	2311
3	1393	2283
4	4354	2283
done	5000	2283

prune458.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
0.4b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
1.0b	(/ 1 (sqrt 3.0))
32.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

170×	`sqrt-prod`
148×	`add-sqr-sqrt`
120×	`times-frac`
83×	`*-un-lft-identity`
75×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
12×	`add-exp-log` `associate-/r*`
11×	`pow1`
10×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`sqrt-div` `div-inv`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-flip` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3-+` `sqrt-unprod` `1-exp` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow`

Counts

4 → 212

Calls

4 calls:

145.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
164.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
12.0ms	(/ 1 (sqrt 3.0))
37.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

series953.0ms

Counts

4 → 10

Calls

4 calls:

291.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
178.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.0ms	(/ 1 (sqrt 3.0))
484.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

simplify3.2s

Counts

222 → 222

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	246	5163
1	448	4821
2	1220	4610
3	4759	4588
done	5000	4588

prune751.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 16.6b

regimes492.0ms

Accuracy

61.6% (7.4b remaining)

Error of 25.7b against oracle of 18.3b and baseline of 37.5b

bsearch66.0ms

Steps

Iters	Range		Point
8	8.450123646982779e+130	1.3503261361162568e+135	9.739776979507706e+134
5	-2.294626366488831e+97	-1.033466382081211e+97	-1.472200864118953e+97

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	34
1	34	34
done	34	34

end0.0ms

sample868.0ms

Algorithm

intervals

Results

548.0ms

8000×

body

valid