Details

sample66.0ms

Algorithm

intervals

Results

26.0ms	48×	body	2560	valid
12.0ms	42×	body	1280	valid
11.0ms	51×	body	640	valid
4.0ms	28×	body	320	valid
3.0ms	72×	body	80	valid
2.0ms	15×	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: 31.5b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite76.0ms

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:

16.0ms	(- 1.0 (cos x))
33.0ms	(/ (- 1.0 (cos x)) (* x x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- 1.0 (cos x))
67.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune297.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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))

rewrite95.0ms

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:

35.0ms	(/ (/ (- 1.0 (cos x)) x) x)
33.0ms	(/ (- 1.0 (cos x)) x)
11.0ms	(- 1.0 (cos x))

series184.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (/ (- 1.0 (cos x)) x) x)
86.0ms	(/ (- 1.0 (cos x)) x)
36.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2993
1	621
0	259

prune658.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

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))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
79×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
53×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `add-cbrt-cube` `unpow3` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `log1p-expm1-u` `flip--`
3×	`pow-unpow` `associate-/r*` `fma-neg`
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 → 183

Calls

4 calls:

46.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
14.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
16.0ms	(pow (- 1.0 (cos x)) 3)
12.0ms	(- 1.0 (cos x))

series167.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
20.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
61.0ms	(pow (- 1.0 (cos x)) 3)
25.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

195 → 195

Iterations

Iter	Nodes
done	5000
2	2912
1	549
0	246

prune670.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.3b	(pow (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) 3)
0.4b	(+ 1.0 (cos x))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

310×	`add-sqr-sqrt`
241×	`unpow-prod-down` `cube-prod`
214×	`*-un-lft-identity`
150×	`times-frac`
144×	`prod-diff`
142×	`add-cube-cbrt`
112×	`difference-of-squares`
83×	`sqr-pow`
35×	`distribute-lft-out--`
27×	`cube-mult` `unpow3`
12×	`fma-neg`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`difference-cubes`
6×	`pow1` `pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `pow-exp` `rem-cube-cbrt`
2×	`pow-to-exp` `pow-pow` `div-inv`
1×	`cube-div` `cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `flip-+` `flip--` `distribute-lft-out`

Counts

4 → 414

Calls

4 calls:

5.0ms	(pow (cos x) 3)
82.0ms	(pow (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) 3)
17.0ms	(+ 1.0 (cos x))
42.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series403.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(pow (cos x) 3)
284.0ms	(pow (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) 3)
18.0ms	(+ 1.0 (cos x))
60.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify871.0ms

Counts

426 → 426

Iterations

Iter	Nodes
done	5000
1	1815
0	457

prune859.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

regimes172.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch107.0ms

Steps

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

simplify2.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	1675×	body	2560	valid
580.0ms	1222×	body	1280	valid
452.0ms	1493×	body	640	valid
209.0ms	894×	body	320	valid
159.0ms	2213×	body	80	valid
132.0ms	503×	body	160	valid