Details

sample112.0ms

Algorithm

intervals

Results

54.0ms	57×	body	2560	valid
16.0ms	34×	body	1280	valid
15.0ms	41×	body	640	valid
8.0ms	36×	body	320	valid
5.0ms	70×	body	80	valid
3.0ms	18×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize10.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
16.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

11.0ms	(- 1.0 (cos x))
36.0ms	(/ (- 1.0 (cos x)) (* x x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- 1.0 (cos x))
76.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.3s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune311.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite55.0ms

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-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

19.0ms	(/ (/ (- 1.0 (cos x)) x) x)
23.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series150.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (/ (- 1.0 (cos x)) x) x)
50.0ms	(/ (- 1.0 (cos x)) x)
27.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2993
1	621
0	259

prune737.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `log-div` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `fma-neg`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

33.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
6.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series200.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
22.0ms	(exp (log (- 1.0 (cos x))))
87.0ms	(log (- 1.0 (cos x)))
25.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1388
1	379
0	201

prune514.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (* (- 1.0 (cos x)) (- 1.0 (cos x))) (- 1.0 (cos x))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`flip3--` `flip--`
28×	`frac-times`
27×	`prod-diff`
26×	`cbrt-div`
25×	`add-cube-cbrt`
14×	`associate-*l/`
10×	`add-log-exp`
9×	`fma-neg`
8×	`associate-*r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 122

Calls

4 calls:

53.0ms	(cbrt (* (* (- 1.0 (cos x)) (- 1.0 (cos x))) (- 1.0 (cos x))))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series111.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (* (* (- 1.0 (cos x)) (- 1.0 (cos x))) (- 1.0 (cos x))))
32.0ms	(- 1.0 (cos x))
33.0ms	(- 1.0 (cos x))
25.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	1937
1	369
0	168

prune530.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes106.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.6b

bsearch82.0ms

Steps

Iters	Range		Point
10	2.777137017098532e-16	1126.7541422477805	0.030783396840863963
9	-0.042530208599811804	-3.2052418334402957e-07	-0.034740631507421044

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1629×	body	2560	valid
1.1s	1270×	body	1280	valid
509.0ms	1487×	body	640	valid
225.0ms	934×	body	320	valid
219.0ms	2187×	body	80	valid
64.0ms	493×	body	160	valid