Details

sample125.0ms

Algorithm

intervals

Results

61.0ms	52×	body	2560	valid
36.0ms	92×	body	1280	valid
12.0ms	57×	body	640	valid
5.0ms	33×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.2b	(- 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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify34.0ms

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460
done	5002	460

prune173.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)))
2.2b	(- 1.0 (cos x))

rewrite49.0ms

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--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 177

Calls

3 calls:

17.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
16.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series94.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
36.0ms	(/ (sin x) (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify69.0ms

Counts

186 → 186

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	572	1779
1	2636	1549
2	5001	1441
done	5001	1441

prune279.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
2.2b	(- 1.0 (cos x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-/r` `flip--` `log1p-expm1-u` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (sin x))
33.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
7.0ms	(- 1.0 (cos x))

series73.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1 (sin x))
39.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
19.0ms	(- 1.0 (cos x))

simplify46.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	728
1	1613	574
2	5002	548
done	5002	548

prune201.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
112×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
86×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos`
1×	`difference-cubes` `+-commutative` `pow2` `pow-to-exp` `sub-neg` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-pow` `fma-def` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 262

Calls

4 calls:

13.0ms	(* (cos x) (cos x))
3.0ms	(pow (cos x) 3)
13.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
30.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series137.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (cos x) (cos x))
27.0ms	(pow (cos x) 3)
46.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify141.0ms

Counts

274 → 274

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	656	2815
1	2754	1911
2	5001	1872
done	5001	1872

prune311.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes70.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.8b

bsearch87.0ms

Steps

Iters	Range		Point
10	0.00012253353073063669	15794870057.515802	0.023153738150023005
9	-2.7342232818785663	-5.599255928070541e-06	-0.02490049914676042

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	39
1	41	39
done	41	39

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1626×	body	2560	valid
1.2s	2815×	body	1280	valid
397.0ms	1799×	body	640	valid
131.0ms	915×	body	320	valid
50.0ms	494×	body	160	valid
28.0ms	348×	body	80	valid
13.0ms	3×	body	5120	valid