Details

sample180.0ms

Algorithm

intervals

Results

83.0ms	48×	body	2560	valid
63.0ms	97×	body	1280	valid
14.0ms	49×	body	640	valid
6.0ms	32×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	13×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

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

series81.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
3	2334
2	774
1	308
0	134

prune459.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (fma x (* 1/24 x) 1/2) (* 1/240 (pow x 5)))
0.0b	(* 1/240 (pow x 5))
0.1b	(fma x (* 1/24 x) 1/2)
0.4b	(* 1/24 x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`add-exp-log`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube`
6×	`pow1` `associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `cbrt-unprod` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-prod-down` `pow-exp`

Counts

4 → 67

Calls

4 calls:

0.0ms	(fma x (fma x (* 1/24 x) 1/2) (* 1/240 (pow x 5)))
9.0ms	(* 1/240 (pow x 5))
0.0ms	(fma x (* 1/24 x) 1/2)
6.0ms	(* 1/24 x)

series294.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma x (fma x (* 1/24 x) 1/2) (* 1/240 (pow x 5)))
81.0ms	(* 1/240 (pow x 5))
113.0ms	(fma x (* 1/24 x) 1/2)
18.0ms	(* 1/24 x)

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	1527
2	493
1	220
0	110

prune461.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.3b	(exp (log (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite50.0ms

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:

26.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
5.0ms	(log (- 1.0 (cos x)))
6.0ms	(exp (log (- 1.0 (cos x))))
6.0ms	(- 1.0 (cos x))

series235.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
135.0ms	(log (- 1.0 (cos x)))
29.0ms	(exp (log (- 1.0 (cos x))))
26.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
3	2247
2	829
1	368
0	200

prune743.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.3b	(pow E (log (- 1.0 (cos x))))
2.1b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
9×	`prod-diff`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `flip3--` `div-exp` `pow-exp` `log1p-expm1-u` `flip--` `pow-sub`
3×	`associate-/r*` `fma-neg`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `div-inv`

Counts

4 → 144

Calls

4 calls:

17.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
6.0ms	(log (- 1.0 (cos x)))
11.0ms	(pow E (log (- 1.0 (cos x))))
12.0ms	(- 1.0 (cos x))

series821.0ms

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
140.0ms	(log (- 1.0 (cos x)))
294.0ms	(pow E (log (- 1.0 (cos x))))
40.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
3	4271
2	1296
1	507
0	246

prune767.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

regimes355.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.1b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	34
2	34
1	32
0	28

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.5s	1586×	body	2560	valid
3.3s	2748×	body	1280	valid
983.0ms	1855×	body	640	valid
544.0ms	495×	body	160	valid
365.0ms	945×	body	320	valid
42.0ms	364×	body	80	valid
37.0ms	7×	body	5120	valid