Details

sample54.0ms

Algorithm

intervals

Results

24.0ms	57×	body	2560	valid
9.0ms	41×	body	1280	valid
8.0ms	59×	body	640	valid
2.0ms	23×	body	320	valid
2.0ms	63×	body	80	valid
1.0ms	13×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
17.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite18.0ms

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))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.4s

Counts

64 → 64

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	116	808
1	272	678
2	870	566
3	4566	526
done	5001	525

prune132.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/720 (pow x 4) 1/2)
11.8b	(fma (pow x 2) -1/24 (fma 1/720 (pow x 4) 1/2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/720 (pow x 4) 1/2)
0.0ms	(fma (pow x 2) -1/24 (fma 1/720 (pow x 4) 1/2))

series126.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 1/720 (pow x 4) 1/2)
43.0ms	(fma (pow x 2) -1/24 (fma 1/720 (pow x 4) 1/2))

simplify1.9s

Counts

26 → 26

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	34	298
1	53	292
2	158	255
3	572	255
4	3418	255
done	5000	255

prune77.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.2b	(- 1.0 (cos x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
46×	`times-frac`
36×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `prod-diff`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `fma-neg` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 132

Calls

3 calls:

8.0ms	(/ (- 1.0 (cos x)) x)
22.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms	(- 1.0 (cos x))

series108.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (- 1.0 (cos x)) x)
46.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
19.0ms	(- 1.0 (cos x))

simplify810.0ms

Counts

141 → 141

Iterations

Useful iterations: 2 (254.0ms)

Iter	Nodes	Cost
0	219	1855
1	577	1581
2	1908	1364
done	5001	1364

prune247.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (expm1 (- 1.0 (cos x))))
0.1b	(* (/ 1 x) (/ (log1p (expm1 (- 1.0 (cos x)))) x))
0.2b	(expm1 (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
26×	`add-exp-log`
25×	`add-cube-cbrt` `times-frac`
16×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`prod-diff`
8×	`div-exp` `prod-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`log1p-expm1-u`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod`
3×	`fma-neg`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `log1p-expm1` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

0.0ms	(log1p (expm1 (- 1.0 (cos x))))
12.0ms	(* (/ 1 x) (/ (log1p (expm1 (- 1.0 (cos x)))) x))
0.0ms	(expm1 (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series412.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(log1p (expm1 (- 1.0 (cos x))))
178.0ms	(* (/ 1 x) (/ (log1p (expm1 (- 1.0 (cos x)))) x))
66.0ms	(expm1 (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify778.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	200	1678
1	496	1262
2	1588	1063
done	5000	1063

prune232.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes46.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.5b

bsearch75.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	0.024083451253618247
10	-64880754058.88788	-2.651420353119469e-05	-0.02660967226737158

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	41
1	32	41
done	32	41

end0.0ms

sample1.6s

Algorithm

intervals

Results

746.0ms	1660×	body	2560	valid
289.0ms	1248×	body	1280	valid
208.0ms	1448×	body	640	valid
98.0ms	918×	body	320	valid
85.0ms	2275×	body	80	valid
32.0ms	451×	body	160	valid