Details

sample119.0ms

Algorithm

intervals

Results

49.0ms	50×	body	2560	valid
20.0ms	40×	body	1280	valid
17.0ms	52×	body	640	valid
8.0ms	34×	body	320	valid
6.0ms	66×	body	80	valid
2.0ms	14×	body	160	valid

simplify61.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize19.0ms

Local error

Found 2 expressions with local error:

1.1b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

series136.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- 1.0 (cos x))
100.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.5s

Counts

64 → 64

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	116	808
1	301	681
2	1709	566
done	5001	553

prune392.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.1b	(- 1.0 (cos x))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
31.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(- 1.0 (cos x))

series191.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (/ (- 1.0 (cos x)) x) x)
79.0ms	(/ (- 1.0 (cos x)) x)
38.0ms	(- 1.0 (cos x))

simplify2.6s

Counts

174 → 174

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	259	2577
1	621	2361
2	2999	2187
done	5000	2152

prune960.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
0.1b	(/ x (- 1.0 (cos x)))
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
1.1b	(- 1.0 (cos x))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

774×	`times-frac`
450×	`add-sqr-sqrt` `*-un-lft-identity`
344×	`add-cube-cbrt`
74×	`associate-/l*`
53×	`distribute-lft-out--` `difference-of-squares`
39×	`associate-/r/`
36×	`add-exp-log`
29×	`associate-/r*`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
18×	`flip3--` `flip--`
10×	`cbrt-undiv`
9×	`prod-diff`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`frac-2neg` `fma-neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `associate-/l/` `inv-pow`

Counts

4 → 475

Calls

4 calls:

81.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
25.0ms	(/ x (- 1.0 (cos x)))
50.0ms	(/ 1 (/ x (- 1.0 (cos x))))
15.0ms	(- 1.0 (cos x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (/ 1 (/ x (- 1.0 (cos x)))) x)
78.0ms	(/ x (- 1.0 (cos x)))
79.0ms	(/ 1 (/ x (- 1.0 (cos x))))
32.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

487 → 487

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	675	9667
1	1903	8194
done	5000	7687

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (/ x (- 1.0 (cos x)))) (/ 1 x))
0.1b	(/ x (- 1.0 (cos x)))
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
1.1b	(- 1.0 (cos x))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

283×	`times-frac`
234×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
135×	`add-cube-cbrt`
100×	`add-exp-log`
68×	`associate-l`
50×	`div-exp`
32×	`add-cbrt-cube`
28×	`prod-exp`
26×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
17×	`rec-exp` `1-exp`
15×	`unswap-sqr`
13×	`cbrt-undiv` `associate-r`
11×	`div-inv`
9×	`pow1` `flip3--` `prod-diff` `flip--`
6×	`cbrt-unprod` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-flip` `fma-neg` `pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sub-neg` `diff-log` `associate-r/` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 324

Calls

4 calls:

117.0ms	(* (/ 1 (/ x (- 1.0 (cos x)))) (/ 1 x))
17.0ms	(/ x (- 1.0 (cos x)))
28.0ms	(/ 1 (/ x (- 1.0 (cos x))))
20.0ms	(- 1.0 (cos x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ 1 (/ x (- 1.0 (cos x)))) (/ 1 x))
77.0ms	(/ x (- 1.0 (cos x)))
79.0ms	(/ 1 (/ x (- 1.0 (cos x))))
29.0ms	(- 1.0 (cos x))

simplify958.0ms

Counts

336 → 336

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	417	5252
1	1351	4486
done	5000	4067

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes150.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.5b

bsearch158.0ms

Steps

Iters	Range		Point
10	2.8868360106527892e-08	453261925.93168354	0.029848537881546774
9	-4.26929226401081	-3.26160511802404e-08	-0.030963531967900033

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	26	44
1	32	33
done	32	33

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	1562×	body	2560	valid
800.0ms	1238×	body	1280	valid
746.0ms	932×	body	320	valid
615.0ms	1516×	body	640	valid
325.0ms	2301×	body	80	valid
80.0ms	451×	body	160	valid