Details

sample50.0ms

Algorithm

intervals

Results

22.0ms	52×	body	2560	valid
8.0ms	41×	body	1280	valid
6.0ms	45×	body	640	valid
3.0ms	33×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
14.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

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:

7.0ms	(- 1.0 (cos x))
20.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify30.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317
done	5001	317

prune128.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`times-frac`
40×	`sqrt-prod`
18×	`prod-diff`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`fma-neg` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 158

Calls

4 calls:

15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
7.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series220.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
19.0ms	(- 1.0 (cos x))
23.0ms	(- 1.0 (cos x))

simplify175.0ms

Counts

170 → 170

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	301	1368
1	936	1148
2	4953	1118
3	5001	1112
done	5001	1112

prune360.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.9b	(/ (cos x) (* x x))
0.9b	(/ 1.0 (* x x))
16.9b	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 125

Calls

3 calls:

11.0ms	(/ (cos x) (* x x))
7.0ms	(/ 1.0 (* x x))
39.0ms	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series136.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (cos x) (* x x))
25.0ms	(/ 1.0 (* x x))
76.0ms	(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify48.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	463	1827
1	1528	1288
2	5001	1186
done	5001	1186

prune195.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
31.0b	(fma (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) x) (- (* (/ (cbrt (cos x)) x) (/ (* (cbrt (cos x)) (cbrt (cos x))) x))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
0.0ms	(fma (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) x) (- (* (/ (cbrt (cos x)) x) (/ (* (cbrt (cos x)) (cbrt (cos x))) x))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (cos x))
100.0ms	(cbrt (cos x))
97.0ms	(cbrt (cos x))
211.0ms	(fma (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) x) (- (* (/ (cbrt (cos x)) x) (/ (* (cbrt (cos x)) (cbrt (cos x))) x))))

simplify44.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	112	441
1	332	388
2	1242	380
3	5001	373
done	5001	373

prune219.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

99% (0.3b remaining)

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

bsearch102.0ms

Steps

Iters	Range		Point
10	0.00012253353073063669	15794870057.515802	0.045072563401532637
9	-2.7342232818785663	-5.599255928070541e-06	-0.03585382449127276

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	55
1	53	55
2	55	55
3	55	55
done	55	55

end0.0ms

sample1.7s

Algorithm

intervals

Results

741.0ms	1628×	body	2560	valid
348.0ms	1430×	body	640	valid
270.0ms	1270×	body	1280	valid
93.0ms	912×	body	320	valid
66.0ms	2261×	body	80	valid
39.0ms	499×	body	160	valid