Details

sample122.0ms

Algorithm

intervals

Results

53.0ms	41×	body	2560	valid
42.0ms	98×	body	1280	valid
13.0ms	60×	body	640	valid
4.0ms	27×	body	320	valid
2.0ms	22×	body	160	valid
1.0ms	8×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite12.0ms

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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: 4 (782.0ms)

Iter	Nodes	Cost
0	106	665
1	235	645
2	509	609
3	1161	609
4	3303	608
done	5000	608

prune142.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite39.0ms

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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series131.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
45.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

124 → 124

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	163	1406
1	305	1293
2	618	1220
3	1398	1218
4	3931	1217
done	5000	1217

prune300.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))) (sin x))
0.3b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

543×	`times-frac`
517×	`add-sqr-sqrt`
337×	`*-un-lft-identity`
208×	`difference-of-squares`
205×	`add-cube-cbrt`
159×	`unpow-prod-down` `cube-prod`
105×	`sqr-pow`
81×	`associate-/l*`
65×	`distribute-lft-out--`
13×	`difference-cubes`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `pow-exp` `clear-num` `sum-log` `flip--` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 412

Calls

4 calls:

67.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))) (sin x))
1.0ms	(pow (cos x) 3)
2.0ms	(+ 1.0 (cos x))
17.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series268.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))) (sin x))
30.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
55.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.8s

Counts

424 → 424

Iterations

Useful iterations: 2 (908.0ms)

Iter	Nodes	Cost
0	588	16449
1	1425	15551
2	4602	15381
done	5001	15381

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.0b	(log (exp (pow (cos x) 3)))
1.9b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite36.0ms

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:

1.0ms	(pow (cos x) 3)
3.0ms	(+ 1.0 (cos x))
7.0ms	(log (exp (pow (cos x) 3)))
24.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
33.0ms	(log (exp (pow (cos x) 3)))
48.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify3.1s

Counts

92 → 92

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	140	922
1	290	707
2	837	660
3	4789	660
done	5000	660

prune256.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

regimes170.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 29.8b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	92
1	53	92
done	53	92

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1553×	body	2560	valid
1.2s	2752×	body	1280	valid
437.0ms	1875×	body	640	valid
140.0ms	930×	body	320	valid
53.0ms	497×	body	160	valid
26.0ms	388×	body	80	valid
13.0ms	5×	body	5120	valid