Details

sample197.0ms

Algorithm

intervals

Results

73.0ms	97×	body	1280	valid
73.0ms	40×	body	2560	valid
20.0ms	55×	body	640	valid
13.0ms	37×	body	320	valid
4.0ms	19×	body	160	valid
1.0ms	8×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series68.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- 1.0 (cos x)) (sin x))
23.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune449.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `log-div` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `fma-neg`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

20.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
5.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
33.0ms	(exp (log (- 1.0 (cos x))))
100.0ms	(log (- 1.0 (cos x)))
28.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1284
1	373
0	200

prune664.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.0b	(log (- (pow 1.0 3) (pow (cos x) 3)))
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
132×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
102×	`unpow-prod-down` `cube-prod`
84×	`add-cube-cbrt`
42×	`sqr-pow`
32×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`log-prod`
12×	`fma-neg`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1` `add-exp-log`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`difference-cubes` `log-div` `flip3--` `flip--`
1×	`pow-to-exp` `+-commutative` `sum-log` `sub-neg` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 272

Calls

4 calls:

5.0ms	(+ 1.0 (cos x))
4.0ms	(pow (cos x) 3)
24.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
27.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series261.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ 1.0 (cos x))
51.0ms	(pow (cos x) 3)
138.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.7s

Counts

284 → 284

Iterations

Iter	Nodes
done	5001
2	2988
1	688
0	295

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1.0 (cos x))
1.0b	(log (- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x))))))
1.9b	(exp (log (- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x)))))))
29.4b	(- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x)))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
16×	`log-prod`
15×	`unpow-prod-down` `cube-prod`
12×	`fma-neg` `difference-of-squares`
8×	`exp-sum` `add-log-exp`
7×	`sqr-pow`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `cube-mult` `log-div` `exp-prod` `add-cbrt-cube` `unpow3` `log1p-expm1-u`
3×	`fma-def` `flip3--` `flip--` `distribute-lft-out--`
2×	`exp-diff` `log-pow`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `diff-log` `rem-log-exp` `flip-+` `distribute-lft-out` `expm1-udef` `associate--r-` `rem-exp-log`

Counts

4 → 130

Calls

4 calls:

12.0ms	(+ 1.0 (cos x))
24.0ms	(log (- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x))))))
23.0ms	(exp (log (- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x)))))))
34.0ms	(- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ 1.0 (cos x))
392.0ms	(log (- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x))))))
346.0ms	(exp (log (- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x)))))))
313.0ms	(- (pow 1.0 3) (expm1 (log1p (* (* (cos x) (cos x)) (cos x)))))

simplify2.0s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	1670
1	415
0	199

prune749.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

regimes430.0ms

Accuracy

97.3% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 30.2b

bsearch2.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	50
2	50
1	48
0	41

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.4s	1565×	body	2560	valid
2.5s	2769×	body	1280	valid
922.0ms	1842×	body	640	valid
282.0ms	967×	body	320	valid
109.0ms	473×	body	160	valid
43.0ms	379×	body	80	valid
29.0ms	5×	body	5120	valid