Details

sample138.0ms

Algorithm

intervals

Results

60.0ms	47×	body	2560	valid
46.0ms	88×	body	1280	valid
14.0ms	61×	body	640	valid
6.0ms	38×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	11×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.4b	(- 1.0 (cos x))

rewrite25.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

58 → 58

Iterations

Useful iterations: 4 (752.0ms)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune144.0ms

Pruning

10 alts after pruning (10 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)))
1.8b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.4b	(- 1.0 (cos x))

rewrite72.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
23.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
22.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms	(- 1.0 (cos x))

series146.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
43.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
41.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

124 → 124

Iterations

Useful iterations: 4 (851.0ms)

Iter	Nodes	Cost
0	163	1406
1	304	1293
2	639	1220
3	1394	1218
4	3567	1217
done	5000	1217

prune295.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.8b	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (+ (cos x) 1.0) (cos x)) (* 1.0 1.0))) (sin x))))
2.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac`
417×	`add-sqr-sqrt`
279×	`*-un-lft-identity`
248×	`log-pow`
247×	`exp-prod`
177×	`add-cube-cbrt`
160×	`difference-of-squares`
123×	`unpow-prod-down` `cube-prod`
81×	`sqr-pow`
50×	`distribute-lft-out--`
10×	`difference-cubes`
8×	`add-log-exp`
6×	`pow1` `associate-/r/`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `log-prod`
2×	`div-sub`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 329

Calls

4 calls:

5.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
184.0ms	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (+ (cos x) 1.0) (cos x)) (* 1.0 1.0))) (sin x))))
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series272.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
16.0ms	(+ (cos x) 1.0)
172.0ms	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (+ (cos x) 1.0) (cos x)) (* 1.0 1.0))) (sin x))))
56.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.4s

Counts

341 → 341

Iterations

Useful iterations: 2 (529.0ms)

Iter	Nodes	Cost
0	668	8637
1	1170	7433
2	2771	7333
done	5000	7333

prune938.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.2b	(/ (log (exp (- 1.0 (cos x)))) (sin x))
2.4b	(- 1.0 (cos x))
2.5b	(log (exp (- 1.0 (cos x))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
4×	`exp-sum`
3×	`sub-neg` `exp-diff` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 103

Calls

4 calls:

15.0ms	(exp (- 1.0 (cos x)))
49.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
6.0ms	(- 1.0 (cos x))
16.0ms	(log (exp (- 1.0 (cos x))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(exp (- 1.0 (cos x)))
37.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
24.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

simplify2.0s

Counts

115 → 115

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	160	1341
1	287	1132
2	637	1070
3	1433	1070
4	4019	1069
done	5000	1069

prune212.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes61.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch82.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	0.02338074252416356
10	-21283307590.397102	-3.152803306627408e-07	-0.02278801870830147

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	41
1	34	33
done	34	33

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1602×	body	2560	valid
1.2s	2734×	body	1280	valid
435.0ms	1857×	body	640	valid
159.0ms	949×	body	320	valid
53.0ms	492×	body	160	valid
31.0ms	366×	body	80	valid