Details

sample109.0ms

Algorithm

intervals

Results

41.0ms	45×	body	2560	valid
21.0ms	42×	body	1280	valid
15.0ms	47×	body	640	valid
8.0ms	34×	body	320	valid
7.0ms	68×	body	80	valid
3.0ms	20×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
13.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
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×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

8.0ms	(- 1.0 (cos x))
64.0ms	(/ (- 1.0 (cos x)) (* x x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(- 1.0 (cos x))
77.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.1s

Counts

48 → 48

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	88	507
1	212	489
2	548	441
3	1500	441
done	5000	441

prune150.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
2.4b	(- 1.0 (cos x))

rewrite83.0ms

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-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

26.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(- 1.0 (cos x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- 1.0 (cos x)) x)
82.0ms	(/ (/ (- 1.0 (cos x)) x) x)
36.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

156 → 156

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	229	2262
1	522	2156
2	1254	2046
3	3200	2024
done	5000	2009

prune422.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.3b	(* (cos x) (cos x))
0.5b	(+ 1.0 (cos x))
2.6b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

38.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
12.0ms	(* (cos x) (cos x))
8.0ms	(+ 1.0 (cos x))
16.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
38.0ms	(* (cos x) (cos x))
20.0ms	(+ 1.0 (cos x))
44.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify1.4s

Counts

93 → 93

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	159	1249
1	415	1091
2	1650	954
done	5000	833

prune351.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (cos x)) (/ (* x (+ 1.0 (cos x))) (- 1.0 (cos x))))
0.5b	(+ 1.0 (cos x))
0.5b	(+ 1.0 (cos x))
2.4b	(- 1.0 (cos x))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
66×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*` `associate-/r/`
10×	`add-log-exp`
6×	`flip3--` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `sum-log` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

88.0ms	(/ (+ 1.0 (cos x)) (/ (* x (+ 1.0 (cos x))) (- 1.0 (cos x))))
7.0ms	(+ 1.0 (cos x))
7.0ms	(+ 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series121.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (+ 1.0 (cos x)) (/ (* x (+ 1.0 (cos x))) (- 1.0 (cos x))))
15.0ms	(+ 1.0 (cos x))
19.0ms	(+ 1.0 (cos x))
36.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

128 → 128

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	192	2457
1	461	2289
2	1858	1879
done	5000	1853

prune338.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.9b

bsearch101.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.03328058389703145
9	-1501.2167507114543	-0.006495210018506858	-0.03155884382850993

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	61
1	39	61
done	39	61

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1538×	body	2560	valid
864.0ms	1280×	body	1280	valid
439.0ms	1481×	body	640	valid
207.0ms	957×	body	320	valid
202.0ms	2287×	body	80	valid
105.0ms	457×	body	160	valid