Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	231×	body	80	valid
1.0ms	9×	body	320	valid
1.0ms	6×	body	640	valid
1.0ms	4×	body	1280	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	2560	valid

simplify405.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	8	11
1	20	11
2	66	11
3	206	9
4	392	9
5	428	9
done	428	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (+ z (* 2 (+ x y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
3×	`*-un-lft-identity` `sum-log`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r+` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 14

Calls

1 calls:

26.0ms

(+ x (+ z (* 2 (+ x y))))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(+ x (+ z (* 2 (+ x y))))

simplify1.6s

Counts

17 → 17

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	38	232
1	112	221
2	399	203
3	2286	203
done	5002	203

prune96.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ z (* 2 (+ x y))))
0.0b	(sqrt (+ x (+ z (* 2 (+ x y)))))
0.0b	(sqrt (+ x (+ z (* 2 (+ x y)))))
0.3b	(* (sqrt (+ x (+ z (* 2 (+ x y))))) (sqrt (+ x (+ z (* 2 (+ x y))))))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity` `sqrt-prod`
28×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `sum-log` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+r+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

26.0ms	(+ x (+ z (* 2 (+ x y))))
33.0ms	(sqrt (+ x (+ z (* 2 (+ x y)))))
36.0ms	(sqrt (+ x (+ z (* 2 (+ x y)))))
163.0ms	(* (sqrt (+ x (+ z (* 2 (+ x y))))) (sqrt (+ x (+ z (* 2 (+ x y))))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ x (+ z (* 2 (+ x y))))
136.0ms	(sqrt (+ x (+ z (* 2 (+ x y)))))
130.0ms	(sqrt (+ x (+ z (* 2 (+ x y)))))
92.0ms	(* (sqrt (+ x (+ z (* 2 (+ x y))))) (sqrt (+ x (+ z (* 2 (+ x y))))))

simplify1.7s

Counts

120 → 120

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	130	2683
1	323	1907
2	1622	1759
done	5001	1720

prune561.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))
0.1b	(sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))
0.2b	(* (pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3) (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))))
0.4b	(pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3)

rewrite423.0ms

Algorithm

rewrite-expression-head

Rules

121×	`sqrt-prod`
74×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
36×	`sqrt-div`
29×	`unpow-prod-down` `cube-prod`
26×	`associate-l`
25×	`add-cube-cbrt`
24×	`unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`add-exp-log` `associate-r`
9×	`flip3-+` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube` `distribute-lft-out`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-r/` `associate-l/` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 170

Calls

4 calls:

36.0ms	(sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))
37.0ms	(sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))
293.0ms	(* (pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3) (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))))
43.0ms	(pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3)

series2.1s

Counts

4 → 12

Calls

4 calls:

686.0ms	(sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))
709.0ms	(sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))
103.0ms	(* (pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3) (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))))
627.0ms	(pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3)

simplify2.8s

Counts

182 → 182

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	217	5092
1	650	3805
2	2775	3628
done	5001	3318

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (sqrt (+ (+ x z) (* 2 (+ x y))))) (cbrt (sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))))
0.2b	(cbrt (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))))
0.2b	(cbrt (sqrt (+ (+ x z) (* 2 (+ x y)))))
0.4b	(pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3)

rewrite361.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
60×	`sqrt-div`
49×	`cbrt-prod`
47×	`add-sqr-sqrt`
40×	`cbrt-div`
31×	`*-un-lft-identity`
29×	`flip3-+` `flip-+`
23×	`add-cube-cbrt`
18×	`associate-*r/`
16×	`frac-add`
13×	`associate-r`
12×	`frac-times` `unswap-sqr`
10×	`unpow-prod-down` `cube-prod`
9×	`pow1` `associate-l`
7×	`add-exp-log`
6×	`associate-*l/`
5×	`pow-pow` `add-cbrt-cube`
4×	`sqrt-pow1` `pow1/3` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `pow1/2` `pow-prod-down`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `prod-exp` `*-commutative` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 150

Calls

4 calls:

235.0ms	(* (cbrt (sqrt (+ (+ x z) (* 2 (+ x y))))) (cbrt (sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))))
21.0ms	(cbrt (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))))
42.0ms	(cbrt (sqrt (+ (+ x z) (* 2 (+ x y)))))
47.0ms	(pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3)

series2.1s

Counts

4 → 12

Calls

4 calls:

603.0ms	(* (cbrt (sqrt (+ (+ x z) (* 2 (+ x y))))) (cbrt (sqrt (sqrt (+ x (+ z (* 2 (+ x y))))))))
441.0ms	(cbrt (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))))
414.0ms	(cbrt (sqrt (+ (+ x z) (* 2 (+ x y)))))
614.0ms	(pow (sqrt (sqrt (+ x (+ z (* 2 (+ x y)))))) 3)

simplify3.2s

Counts

162 → 162

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	384	5188
1	1046	4737
2	3764	4583
done	5001	4324

prune1.9s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.0b

regimes340.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
done	12	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	7443×	body	80	valid
103.0ms	204×	body	640	valid
42.0ms	161×	body	1280	valid
17.0ms	113×	body	320	valid
10.0ms	33×	body	2560	valid
7.0ms	65×	body	160	valid