Details

sample60.0ms

Algorithm

intervals

Results

21.0ms	42×	body	2560	valid
11.0ms	40×	body	1280	valid
10.0ms	54×	body	640	valid
4.0ms	34×	body	320	valid
4.0ms	67×	body	80	valid
2.0ms	19×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize12.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
12.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite28.0ms

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:

6.0ms	(- 1.0 (cos x))
20.0ms	(/ (- 1.0 (cos x)) (* x x))

series95.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1.0 (cos x))
73.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune315.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
156×	`times-frac`
104×	`sqrt-prod`
103×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-cbrt-cube` `prod-diff` `add-exp-log` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 238

Calls

4 calls:

14.0ms	(/ (sqrt (- 1.0 (cos x))) x)
83.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
10.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (sqrt (- 1.0 (cos x))) x)
60.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
22.0ms	(- 1.0 (cos x))
40.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

250 → 250

Iterations

Iter	Nodes
done	5000
1	809
0	261

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite115.0ms

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-l`
17×	`add-cbrt-cube`
13×	`associate-r`
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` `associate-/r*` `fma-neg` `log1p-expm1-u` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

3 → 133

Calls

3 calls:

66.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
29.0ms	(/ (- 1.0 (cos x)) x)
11.0ms	(- 1.0 (cos x))

series159.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
77.0ms	(/ (- 1.0 (cos x)) x)
24.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5002
2	3378
1	625
0	219

prune555.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.0b	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))
1.2b	(- 1.0 (cos x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`prod-diff` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos` `sub-neg` `flip3--` `diff-log` `pow3` `flip--`
1×	`pow2` `difference-cubes` `+-commutative` `associate-+l+` `sum-log` `fma-def` `flip3-+` `pow-plus` `distribute-rgt-out` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
12.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
33.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))
11.0ms	(- 1.0 (cos x))

series195.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (cos x) (cos x))
61.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
87.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))
21.0ms	(- 1.0 (cos x))

simplify3.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	3318
1	472
0	172

prune520.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes121.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch83.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.033817197098290584
10	-17239113253358.373	-4.96108325192681e-05	-0.031198749760063066

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	1664×	body	2560	valid
781.0ms	1501×	body	640	valid
482.0ms	1176×	body	1280	valid
236.0ms	941×	body	320	valid
118.0ms	2244×	body	80	valid
100.0ms	474×	body	160	valid