Details

sample118.0ms

Algorithm

intervals

Results

55.0ms	44×	body	2560	valid
36.0ms	88×	body	1280	valid
12.0ms	53×	body	640	valid
5.0ms	32×	body	320	valid
3.0ms	25×	body	160	valid
1.0ms	14×	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: 27.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 1.0 (cos x))

rewrite13.0ms

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))

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	525	609
3	1299	609
4	4031	608
done	5001	608

prune157.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

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))))
1.9b	(- 1.0 (cos x))

rewrite45.0ms

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))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
17.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

124 → 124

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	163	1406
1	305	1293
2	633	1220
3	1531	1218
4	4655	1217
done	5000	1217

prune305.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (/ 1 (sin x)) (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`sub-neg` `flip3--` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `rec-exp` `distribute-lft-in` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

3 → 90

Calls

3 calls:

3.0ms	(/ 1 (sin x))
20.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series70.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1 (sin x))
34.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	150	1020
1	351	878
2	873	782
3	2151	782
done	5001	782

prune199.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

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))))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.7b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite80.0ms

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:

53.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
2.0ms	(pow (cos x) 3)
3.0ms	(+ 1.0 (cos x))
16.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series256.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (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)
14.0ms	(+ 1.0 (cos x))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify823.0ms

Counts

151 → 151

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	219	3074
1	572	2887
2	2196	2723
done	5000	2723

prune356.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.2b

regimes222.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.2b

bsearch84.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	0.024888732994626496
8	-0.04390830018224924	-1.7961213486546931e-06	-0.021181971530877853

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	94
1	58	94
done	58	94

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1609×	body	2560	valid
1.2s	2698×	body	1280	valid
433.0ms	1887×	body	640	valid
360.0ms	953×	body	320	valid
49.0ms	472×	body	160	valid
23.0ms	378×	body	80	valid
13.0ms	3×	body	5120	valid