Details

sample166.0ms

Algorithm

intervals

Results

73.0ms	48×	body	2560	valid
52.0ms	89×	body	1280	valid
20.0ms	62×	body	640	valid
6.0ms	27×	body	320	valid
4.0ms	19×	body	160	valid
1.0ms	11×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite49.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
9.0ms	(- 1.0 (cos x))

series73.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
26.0ms	(- 1.0 (cos x))

simplify505.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune334.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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)))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

125.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
5.0ms	(pow (cos x) 3)
10.0ms	(+ 1.0 (cos x))
45.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series275.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
35.0ms	(pow (cos x) 3)
11.0ms	(+ 1.0 (cos x))
64.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.8s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	2970
1	678
0	258

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
0.8b	(log (exp (pow (cos x) 3)))
1.9b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

3.0ms	(pow (cos x) 3)
5.0ms	(+ 1.0 (cos x))
6.0ms	(log (exp (pow (cos x) 3)))
49.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (cos x) 3)
17.0ms	(+ 1.0 (cos x))
37.0ms	(log (exp (pow (cos x) 3)))
63.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify982.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1501
1	359
0	141

prune609.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (+ (cos x) 1.0) (cos x))))))
0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
81×	`log-prod` `exp-sum`
79×	`*-un-lft-identity`
75×	`times-frac`
64×	`difference-of-squares`
51×	`unpow-prod-down` `cube-prod`
37×	`add-cube-cbrt`
33×	`sqr-pow`
20×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1`
5×	`add-cbrt-cube` `add-exp-log`
4×	`difference-cubes` `exp-prod`
3×	`pow-unpow`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cube-mult` `pow-to-exp` `+-commutative` `log-div` `sum-log` `sub-neg` `pow-pow` `flip3--` `exp-diff` `diff-log` `unpow3` `pow-exp` `log-pow` `div-inv` `flip--` `distribute-lft-out` `rem-cube-cbrt` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

31.0ms	(exp (log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (+ (cos x) 1.0) (cos x))))))
3.0ms	(pow (cos x) 3)
8.0ms	(+ (cos x) 1.0)
38.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series388.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(exp (log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (+ (cos x) 1.0) (cos x))))))
34.0ms	(pow (cos x) 3)
18.0ms	(+ (cos x) 1.0)
93.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.6s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	3335
1	942
0	428

prune794.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes290.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.2b

bsearch2.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	54
1	54
0	44

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.6s	1619×	body	2560	valid
2.1s	2702×	body	1280	valid
1.2s	1905×	body	640	valid
345.0ms	923×	body	320	valid
188.0ms	502×	body	160	valid
37.0ms	345×	body	80	valid
26.0ms	4×	body	5120	valid