Details

sample79.0ms

Algorithm

intervals

Results

39.0ms	48×	body	2560	valid
11.0ms	42×	body	1280	valid
11.0ms	51×	body	640	valid
4.0ms	28×	body	320	valid
3.0ms	72×	body	80	valid
1.0ms	15×	body	160	valid

simplify13.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize10.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
13.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite22.0ms

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:

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

series88.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1.0 (cos x))
67.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify560.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	88	507
1	232	489
2	1129	441
done	5000	441

prune208.0ms

Pruning

9 alts after pruning (9 fresh and 0 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)
2.0b	(- 1.0 (cos x))

rewrite65.0ms

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:

33.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series165.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (/ (- 1.0 (cos x)) x) x)
76.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(- 1.0 (cos x))

simplify1.0s

Counts

156 → 156

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	229	2262
1	549	2156
2	2463	2050
done	5001	2030

prune515.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
0.3b	(pow (- 1.0 (cos x)) 3)
2.0b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
72×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
46×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `add-cbrt-cube` `unpow3` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-unpow` `associate-/r*`
2×	`associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

25.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
7.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
8.0ms	(pow (- 1.0 (cos x)) 3)
5.0ms	(- 1.0 (cos x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
23.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
65.0ms	(pow (- 1.0 (cos x)) 3)
29.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

175 → 175

Iterations

Useful iterations: 2 (462.0ms)

Iter	Nodes	Cost
0	214	2582
1	479	1953
2	2439	1835
done	5001	1835

prune671.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (* (cbrt (pow (- 1.0 (cos x)) 2)) (cbrt (- 1.0 (cos x)))) 3))
0.3b	(pow (* (cbrt (pow (- 1.0 (cos x)) 2)) (cbrt (- 1.0 (cos x)))) 3)
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`cbrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-exp-log`
6×	`cbrt-div` `add-cube-cbrt`
5×	`add-cbrt-cube`
4×	`cube-div` `pow-pow` `flip3--` `associate-*r/` `flip--`
3×	`pow-unpow` `pow1/3`
2×	`cube-mult` `sub-neg` `unpow-prod-down` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `pow3` `prod-exp` `rem-cbrt-cube` `cbrt-unprod` `unpow2`

Counts

4 → 73

Calls

4 calls:

8.0ms	(cbrt (pow (* (cbrt (pow (- 1.0 (cos x)) 2)) (cbrt (- 1.0 (cos x)))) 3))
31.0ms	(pow (* (cbrt (pow (- 1.0 (cos x)) 2)) (cbrt (- 1.0 (cos x)))) 3)
9.0ms	(- 1.0 (cos x))
9.0ms	(- 1.0 (cos x))

series146.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (pow (* (cbrt (pow (- 1.0 (cos x)) 2)) (cbrt (- 1.0 (cos x)))) 3))
60.0ms	(pow (* (cbrt (pow (- 1.0 (cos x)) 2)) (cbrt (- 1.0 (cos x)))) 3)
28.0ms	(- 1.0 (cos x))
32.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

85 → 85

Iterations

Useful iterations: 2 (234.0ms)

Iter	Nodes	Cost
0	118	1280
1	301	828
2	1469	675
done	5001	675

prune404.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes103.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.3b

bsearch87.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.029870589015516296
7	-0.10952899301968014	-0.00181011214377754	-0.029468940558385545

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	37
1	29	30
done	29	30

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.0s	1675×	body	2560	valid
611.0ms	1222×	body	1280	valid
502.0ms	1493×	body	640	valid
178.0ms	894×	body	320	valid
140.0ms	2213×	body	80	valid
75.0ms	503×	body	160	valid