Details

sample111.0ms

Algorithm

intervals

Results

48.0ms	57×	body	2560	valid
17.0ms	44×	body	1280	valid
16.0ms	56×	body	640	valid
6.0ms	57×	body	80	valid
5.0ms	28×	body	320	valid
2.0ms	14×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize36.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
17.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite53.0ms

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` `insert-posit16` `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 → 60

Calls

2 calls:

10.0ms	(- 1.0 (cos x))
38.0ms	(/ (- 1.0 (cos x)) (* x x))

series144.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- 1.0 (cos x))
100.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify6.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3754
2	888
1	294
0	118

prune602.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) (* 1/720 (* x x)) 1/2)
0.2b	(* 1/720 (* x x))
11.0b	(fma (* x x) -1/24 (fma (* x x) (* 1/720 (* x x)) 1/2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

1.0ms	(fma (* x x) (* 1/720 (* x x)) 1/2)
32.0ms	(* 1/720 (* x x))
2.0ms	(fma (* x x) -1/24 (fma (* x x) (* 1/720 (* x x)) 1/2))

series613.0ms

Counts

3 → 9

Calls

3 calls:

475.0ms	(fma (* x x) (* 1/720 (* x x)) 1/2)
50.0ms	(* 1/720 (* x x))
87.0ms	(fma (* x x) -1/24 (fma (* x x) (* 1/720 (* x x)) 1/2))

simplify3.8s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	1963
2	417
1	147
0	70

prune558.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.6b	(- 1.0 (cos x))

rewrite128.0ms

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` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 168

Calls

3 calls:

58.0ms	(/ (/ (- 1.0 (cos x)) x) x)
40.0ms	(/ (- 1.0 (cos x)) x)
11.0ms	(- 1.0 (cos x))

series197.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (/ (- 1.0 (cos x)) x) x)
70.0ms	(/ (- 1.0 (cos x)) x)
43.0ms	(- 1.0 (cos x))

simplify3.3s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	1584
1	601
0	262

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- 1.0 (cos x))) (/ (/ (sqrt (- 1.0 (cos x))) x) x))
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
2.6b	(- 1.0 (cos x))
2.6b	(- 1.0 (cos x))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

190×	`times-frac`
169×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
111×	`add-cube-cbrt`
88×	`associate-r`
76×	`sqrt-prod`
18×	`prod-diff`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-cbrt-cube` `add-exp-log`
8×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
6×	`pow1` `fma-neg` `sqrt-div`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `prod-exp` `cbrt-unprod`
2×	`frac-times` `sub-neg` `diff-log` `associate-*l/` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 237

Calls

4 calls:

134.0ms	(* (sqrt (- 1.0 (cos x))) (/ (/ (sqrt (- 1.0 (cos x))) x) x))
40.0ms	(/ (sqrt (- 1.0 (cos x))) x)
10.0ms	(- 1.0 (cos x))
10.0ms	(- 1.0 (cos x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sqrt (- 1.0 (cos x))) (/ (/ (sqrt (- 1.0 (cos x))) x) x))
145.0ms	(/ (sqrt (- 1.0 (cos x))) x)
42.0ms	(- 1.0 (cos x))
26.0ms	(- 1.0 (cos x))

simplify4.6s

Counts

249 → 249

Iterations

Iter	Nodes
done	5003
2	2691
1	873
0	340

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes139.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 31.9b

bsearch169.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.031106757764091195
10	-26711381.42537418	-6.803810524357175e-07	-0.027405319297458403

simplify17.0ms

Iterations

Iter	Nodes
done	30
1	30
0	27

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1604×	body	2560	valid
939.0ms	1239×	body	1280	valid
384.0ms	1505×	body	640	valid
305.0ms	931×	body	320	valid
127.0ms	2254×	body	80	valid
78.0ms	467×	body	160	valid