Details

sample204.0ms

Algorithm

intervals

Results

76.0ms	42×	body	2560	valid
60.0ms	86×	body	1280	valid
41.0ms	68×	body	640	valid
8.0ms	34×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	8×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite33.0ms

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:

19.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series80.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
33.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune464.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 177

Calls

3 calls:

15.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
20.0ms	(/ (sin x) (- 1.0 (cos x)))
13.0ms	(- 1.0 (cos x))

series160.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
61.0ms	(/ (sin x) (- 1.0 (cos x)))
27.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	3505
1	656
0	269

prune896.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sin x)) (* (+ 1.0 (cos x)) (- 1.0 (cos x))))
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
45×	`prod-diff`
44×	`distribute-rgt-in` `distribute-lft-in` `add-cube-cbrt`
26×	`add-exp-log`
16×	`frac-times` `add-cbrt-cube`
13×	`associate-l`
12×	`prod-exp` `associate-*r/`
10×	`add-log-exp`
9×	`pow1` `times-frac`
8×	`flip3-+` `flip-+`
7×	`flip3--` `flip--`
6×	`fma-def` `cbrt-unprod`
5×	`sub-neg` `associate-*l/`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg` `pow-prod-down`
2×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `distribute-lft-out`
1×	`diff-log` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

68.0ms	(* (/ 1 (sin x)) (* (+ 1.0 (cos x)) (- 1.0 (cos x))))
5.0ms	(+ 1.0 (cos x))
6.0ms	(+ 1.0 (cos x))
9.0ms	(- 1.0 (cos x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ 1 (sin x)) (* (+ 1.0 (cos x)) (- 1.0 (cos x))))
19.0ms	(+ 1.0 (cos x))
20.0ms	(+ 1.0 (cos x))
40.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
1	977
0	290

prune899.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

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)))
0.8b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.2b	(- 1.0 (cos x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

15.0ms	(/ (- 1.0 (cos x)) (sin x))
31.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
31.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- 1.0 (cos x)) (sin x))
70.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
60.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
24.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1390
1	392
0	195

prune625.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes378.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.3b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	40
1	40
0	29

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.6s	1660×	body	2560	valid
2.8s	2710×	body	1280	valid
1.3s	1881×	body	640	valid
548.0ms	474×	body	160	valid
349.0ms	940×	body	320	valid
37.0ms	332×	body	80	valid
16.0ms	3×	body	5120	valid