Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

350×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	17	7
3	21	7
4	23	7
5	24	7
done	24	7

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ (- (* x x) 3.0) 6.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`times-frac`
10×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-/l*` `difference-of-squares`
3×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`associate-/l/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 36

Calls

1 calls:

9.0ms

(/ (- (* x x) 3.0) 6.0)

series67.0ms

Counts

1 → 3

Calls

1 calls:

67.0ms

(/ (- (* x x) 3.0) 6.0)

simplify2.6s

Counts

39 → 39

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	80	467
1	181	451
2	438	419
3	1212	419
4	4305	418
done	5001	418

prune76.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* 0.16666666666666666 (pow x 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-l` `prod-exp` `add-cbrt-cube`
2×	`unpow2` `sqr-pow`
1×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

6.0ms

(* 0.16666666666666666 (pow x 2))

series28.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(* 0.16666666666666666 (pow x 2))

simplify2.7s

Counts

32 → 32

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	53	244
1	110	221
2	280	188
3	729	188
4	3164	185
done	5001	185

prune52.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.2b	(* x (sqrt 0.16666666666666666))
0.2b	(* x (sqrt 0.16666666666666666))
0.3b	(* (* x (sqrt 0.16666666666666666)) (* x (sqrt 0.16666666666666666)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
19×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
17×	`add-sqr-sqrt`
13×	`associate-r`
10×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-prod`
7×	`associate-l`
4×	`pow-sqr` `pow-prod-up` `unswap-sqr`
3×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`pow-plus`
1×	`pow2` `swap-sqr`

Counts

3 → 84

Calls

3 calls:

4.0ms	(* x (sqrt 0.16666666666666666))
4.0ms	(* x (sqrt 0.16666666666666666))
15.0ms	(* (* x (sqrt 0.16666666666666666)) (* x (sqrt 0.16666666666666666)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* x (sqrt 0.16666666666666666))
44.0ms	(* x (sqrt 0.16666666666666666))
70.0ms	(* (* x (sqrt 0.16666666666666666)) (* x (sqrt 0.16666666666666666)))

simplify3.7s

Counts

93 → 93

Iterations

Useful iterations: 3 (360.0ms)

Iter	Nodes	Cost
0	64	731
1	137	542
2	419	456
3	1437	451
done	5001	451

prune122.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sqrt 3.0)) 6.0)
0.0b	(- x (sqrt 3.0))
0.0b	(+ (sqrt 3.0) x)
0.7b	(* (+ (sqrt 3.0) x) (/ (- x (sqrt 3.0)) 6.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
41×	`add-cube-cbrt`
37×	`times-frac`
22×	`associate-r`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `fma-def` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`flip3-+` `fma-neg` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 150

Calls

4 calls:

13.0ms	(/ (- x (sqrt 3.0)) 6.0)
4.0ms	(- x (sqrt 3.0))
5.0ms	(+ (sqrt 3.0) x)
36.0ms	(* (+ (sqrt 3.0) x) (/ (- x (sqrt 3.0)) 6.0))

series502.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (- x (sqrt 3.0)) 6.0)
41.0ms	(- x (sqrt 3.0))
228.0ms	(+ (sqrt 3.0) x)
166.0ms	(* (+ (sqrt 3.0) x) (/ (- x (sqrt 3.0)) 6.0))

simplify990.0ms

Counts

162 → 162

Iterations

Useful iterations: 2 (337.0ms)

Iter	Nodes	Cost
0	196	2111
1	457	1744
2	1550	1522
done	5001	1522

prune256.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	8	7
done	8	7

end0.0ms

sample301.0ms

Algorithm

intervals

Results

187.0ms

10627×

body

valid