Details

sample206.0ms

Algorithm

intervals

Results

129.0ms	862×	body	80	nan
39.0ms	296×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
5	2003
4	806
3	225
2	76
1	30
0	14

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
7.2b	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
24×	`associate-r` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
9×	`associate-l` `associate-*r/`
8×	`sqrt-prod`
6×	`flip3--` `sqrt-div` `flip--`
4×	`associate-/r*` `associate-/r/` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `sub-neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `associate-l/` `-commutative` `div-inv` `distribute-lft-out--`
1×	`clear-num` `frac-2neg` `pow1/2`

Counts

4 → 121

Calls

4 calls:

38.0ms	(* 9 (- a (/ 1.0 3.0)))
7.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
10.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
62.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

series415.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* 9 (- a (/ 1.0 3.0)))
76.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
132.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
147.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

simplify925.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	624
0	249

prune602.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
0.0b	(sqrt (- a (/ 1.0 3.0)))
0.3b	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
7.2b	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
356×	`add-sqr-sqrt`
252×	`*-un-lft-identity`
194×	`add-cube-cbrt`
170×	`sqrt-prod`
123×	`associate-r`
58×	`difference-of-squares`
29×	`distribute-lft-out--`
21×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
14×	`flip3--` `flip--`
13×	`associate-/l*`
10×	`frac-add`
9×	`associate-/r*` `add-log-exp`
7×	`pow1`
6×	`frac-times` `cbrt-undiv` `sqrt-div` `div-exp` `associate-l` `associate-*l/`
5×	`unswap-sqr`
4×	`associate-/r/` `insert-posit16`
3×	`prod-exp` `associate-*r/` `cbrt-unprod`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `associate-+l-` `flip-+` `associate-/l/`

Counts

4 → 357

Calls

4 calls:

50.0ms	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
14.0ms	(sqrt (- a (/ 1.0 3.0)))
19.0ms	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
46.0ms	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
74.0ms	(sqrt (- a (/ 1.0 3.0)))
161.0ms	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
185.0ms	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

simplify1.4s

Counts

369 → 369

Iterations

Iter	Nodes
done	2002
2	2002
1	1522
0	558

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(- (/ 1.0 3.0) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
7.2b	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
356×	`add-sqr-sqrt`
252×	`*-un-lft-identity`
194×	`add-cube-cbrt`
170×	`sqrt-prod`
123×	`associate-r`
58×	`difference-of-squares`
29×	`distribute-lft-out--`
21×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
9×	`associate-/r*`
8×	`flip3--` `flip--`
7×	`pow1`
6×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-l` `add-log-exp`
5×	`frac-sub` `unswap-sqr`
4×	`frac-times` `associate-*l/` `associate-/r/` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`associate-*r/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 349

Calls

4 calls:

14.0ms	(sqrt (- a (/ 1.0 3.0)))
17.0ms	(- (/ 1.0 3.0) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
14.0ms	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
78.0ms	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (- a (/ 1.0 3.0)))
172.0ms	(- (/ 1.0 3.0) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
132.0ms	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
200.0ms	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

simplify1.2s

Counts

361 → 361

Iterations

Iter	Nodes
done	2001
2	2001
1	1420
0	529

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))))
0.3b	(/ (/ rand 3) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))))
3.8b	(* (/ (- a (/ 1.0 3.0)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0))))) (/ (/ rand 3) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

843×	`add-sqr-sqrt`
822×	`times-frac`
662×	`sqrt-prod`
505×	`*-un-lft-identity`
307×	`add-cube-cbrt`
202×	`difference-of-squares`
188×	`associate-r`
73×	`distribute-lft-out--`
54×	`associate-l`
33×	`div-inv`
32×	`add-cbrt-cube` `add-exp-log`
26×	`distribute-lft-out`
22×	`associate-/r*`
19×	`associate-/l*`
15×	`unswap-sqr`
13×	`cbrt-undiv` `div-exp`
10×	`sqrt-div`
8×	`associate-/r/`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`flip3--` `insert-posit16` `flip--` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 613

Calls

4 calls:

15.0ms	(sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))
35.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))))
18.0ms	(/ (/ rand 3) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))))
115.0ms	(* (/ (- a (/ 1.0 3.0)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0))))) (/ (/ rand 3) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))))

series57.6s

Counts

4 → 12

Calls

4 calls:

247.0ms	(sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))
594.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))))
949.0ms	(/ (/ rand 3) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))))
55.8s	(* (/ (- a (/ 1.0 3.0)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0))))) (/ (/ rand 3) (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0))))))

simplify6.1s

Counts

625 → 625

Iterations

Iter	Nodes
done	2001
1	2001
0	870

prune3.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes120.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.2s	26837×	body	80	nan
1.7s	9085×	body	80	valid