Details

sample142.0ms

Algorithm

intervals

Results

54.0ms	56×	body	2560	valid
27.0ms	59×	body	80	valid
21.0ms	42×	body	1280	valid
14.0ms	45×	body	640	valid
9.0ms	38×	body	320	valid
3.0ms	16×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
16.0ms	(/ (- 1.0 (cos x)) (* x x))

series156.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- 1.0 (cos x))
117.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify666.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune237.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/720 (* x x)) -1/24)
0.2b	(* (* x x) (+ (* 1/720 (* x x)) -1/24))
0.2b	(* 1/720 (* x x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
2×	`flip3-+` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`

Counts

3 → 53

Calls

3 calls:

24.0ms	(+ (* 1/720 (* x x)) -1/24)
56.0ms	(* (* x x) (+ (* 1/720 (* x x)) -1/24))
17.0ms	(* 1/720 (* x x))

series287.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(+ (* 1/720 (* x x)) -1/24)
154.0ms	(* (* x x) (+ (* 1/720 (* x x)) -1/24))
43.0ms	(* 1/720 (* x x))

simplify1.7s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	2132
1	292
0	86

prune273.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

29.0ms	(/ (/ (- 1.0 (cos x)) x) x)
16.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (/ (- 1.0 (cos x)) x) x)
73.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	2463
1	549
0	229

prune614.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.2b	(* (cos x) (cos x))
0.3b	(+ 1.0 (cos x))
2.2b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
8×	`add-log-exp`
4×	`times-frac` `associate-/l*`
3×	`swap-sqr` `associate-r` `associate-l` `difference-of-squares`
2×	`cbrt-undiv` `sqr-cos` `flip3-+` `flip3--` `div-exp` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `flip--` `associate-/l/`
1×	`pow2` `+-commutative` `clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `div-inv` `distribute-lft-out` `associate--r+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

20.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
8.0ms	(* (cos x) (cos x))
5.0ms	(+ 1.0 (cos x))
6.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
23.0ms	(* (cos x) (cos x))
15.0ms	(+ 1.0 (cos x))
40.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	3371
1	481
0	160

prune466.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes176.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 32.0b

bsearch124.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	0.022350989698977898
10	-1138.2876542095912	-1.6260248627107784e-07	-0.03428006622296721

simplify4.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	1580×	body	2560	valid
674.0ms	1234×	body	1280	valid
426.0ms	1494×	body	640	valid
232.0ms	2260×	body	80	valid
218.0ms	946×	body	320	valid
62.0ms	486×	body	160	valid