Details

sample270.0ms

Algorithm

intervals

Results

111.0ms	48×	body	2560	valid
98.0ms	89×	body	1280	valid
31.0ms	62×	body	640	valid
9.0ms	27×	body	320	valid
5.0ms	19×	body	160	valid
1.0ms	11×	body	80	valid

simplify12.0ms

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: 30.5b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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:

30.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune415.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
144×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
113×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r*` `fma-def`
2×	`flip3--` `flip--` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `pow-exp` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 354

Calls

4 calls:

126.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
5.0ms	(pow (cos x) 3)
7.0ms	(+ (cos x) 1.0)
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series323.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
43.0ms	(pow (cos x) 3)
19.0ms	(+ (cos x) 1.0)
94.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify3.2s

Counts

366 → 366

Iterations

Iter	Nodes
done	5000
2	4314
1	921
0	380

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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:

4.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
30.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series304.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(pow (cos x) 3)
20.0ms	(+ (cos x) 1.0)
176.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
68.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.6s

Counts

284 → 284

Iterations

Iter	Nodes
done	5000
2	3082
1	693
0	297

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 266

Calls

4 calls:

10.0ms	(+ 1.0 (cos x))
29.0ms	(log (exp (+ 1.0 (cos x))))
48.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
50.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series309.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ 1.0 (cos x))
19.0ms	(log (exp (+ 1.0 (cos x))))
174.0ms	(log (- (pow 1.0 3) (pow (cos x) 3)))
98.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.5s

Counts

278 → 278

Iterations

Iter	Nodes
done	5000
2	2566
1	650
0	304

prune967.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes337.0ms

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	45
1	45
0	41

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.1s	1619×	body	2560	valid
2.6s	2702×	body	1280	valid
899.0ms	1905×	body	640	valid
447.0ms	502×	body	160	valid
276.0ms	923×	body	320	valid
78.0ms	345×	body	80	valid
17.0ms	4×	body	5120	valid