Details

sample126.0ms

Algorithm

intervals

Results

64.0ms	44×	body	2560	valid
31.0ms	77×	body	1280	valid
14.0ms	66×	body	640	valid
6.0ms	38×	body	320	valid
2.0ms	17×	body	80	valid
1.0ms	14×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

16.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(- 1.0 (cos x))

simplify78.0ms

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373
done	5001	373

prune152.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ (cos x) 1.0))
0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

24.0ms	(* (cos x) (+ (cos x) 1.0))
3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series118.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (cos x) (+ (cos x) 1.0))
32.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify66.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	353	593
1	1734	555
2	5001	535
done	5001	535

prune260.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

16.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
25.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms	(- 1.0 (cos x))

series140.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
49.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify87.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766
done	5001	766

prune308.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.0b	(log (exp (pow (cos x) 3)))
1.3b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
7.0ms	(log (exp (pow (cos x) 3)))
37.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
28.0ms	(log (exp (pow (cos x) 3)))
51.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify40.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	296	446
1	1109	381
2	5001	373
done	5001	373

prune248.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes74.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.5b

bsearch78.0ms

Steps

Iters	Range		Point
8	0.016621422887445694	5.276955647516397	0.020904349932135746
9	-0.05800990145057735	-1.1864783425707322e-08	-0.02322762662824426

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	37
1	46	37
done	46	37

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1604×	body	2560	valid
1.2s	2719×	body	1280	valid
447.0ms	1920×	body	640	valid
139.0ms	940×	body	320	valid
56.0ms	460×	body	160	valid
30.0ms	354×	body	80	valid
18.0ms	3×	body	5120	valid