Details

sample130.0ms

Algorithm

intervals

Results

66.0ms	50×	body	2560	valid
39.0ms	94×	body	1280	valid
12.0ms	58×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	12×	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: 30.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
3.4b	(- 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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series51.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

58 → 58

Iterations

Useful iterations: 4 (811.0ms)

Iter	Nodes	Cost
0	106	665
1	235	645
2	525	609
3	1298	609
4	4026	608
done	5000	608

prune153.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
2.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.4b	(- 1.0 (cos x))

rewrite38.0ms

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))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series134.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
22.0ms	(- 1.0 (cos x))

simplify2.4s

Counts

124 → 124

Iterations

Useful iterations: 4 (930.0ms)

Iter	Nodes	Cost
0	163	1406
1	305	1293
2	633	1220
3	1530	1218
4	4626	1217
done	5000	1217

prune285.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.1b	(/ (cos x) (sin x))
3.6b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

2.0ms	(/ 1.0 (sin x))
3.0ms	(/ (cos x) (sin x))
20.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1.0 (sin x))
18.0ms	(/ (cos x) (sin x))
80.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: 4 (634.0ms)

Iter	Nodes	Cost
0	146	963
1	289	920
2	610	873
3	1421	873
4	3480	870
done	5000	870

prune227.0ms

Pruning

12 alts after pruning (11 fresh and 1 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)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
3.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `associate-*r/` `div-exp` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

46.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
1.0ms	(pow (cos x) 3)
5.0ms	(+ 1.0 (cos x))
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series256.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
27.0ms	(pow (cos x) 3)
9.0ms	(+ 1.0 (cos x))
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify740.0ms

Counts

151 → 151

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	219	3074
1	572	2887
2	2197	2723
done	5000	2723

prune345.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes108.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch78.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.02572971521680811
10	-155084744.97222546	-0.0009113054925467739	-0.020168669770568547

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	46
1	35	46
done	35	46

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	1649×	body	2560	valid
1.2s	2670×	body	1280	valid
455.0ms	1833×	body	640	valid
274.0ms	494×	body	160	valid
154.0ms	952×	body	320	valid
30.0ms	6×	body	5120	valid
28.0ms	396×	body	80	valid