Details

sample86.0ms

Algorithm

intervals

Results

29.0ms	42×	body	2560	valid
15.0ms	40×	body	1280	valid
14.0ms	54×	body	640	valid
7.0ms	34×	body	320	valid
5.0ms	67×	body	80	valid
2.0ms	19×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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

series114.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- 1.0 (cos x))
80.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4103
2	936
1	290
0	116

prune297.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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))

rewrite146.0ms

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:

24.0ms	(/ (sqrt (- 1.0 (cos x))) x)
80.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
10.0ms	(- 1.0 (cos x))
11.0ms	(- 1.0 (cos x))

series207.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (sqrt (- 1.0 (cos x))) x)
52.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
20.0ms	(- 1.0 (cos x))
29.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

250 → 250

Iterations

Iter	Nodes
done	5001
2	2357
1	797
0	261

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite85.0ms

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:

36.0ms	(/ (/ (- 1.0 (cos x)) x) x)
27.0ms	(/ (- 1.0 (cos x)) x)
10.0ms	(- 1.0 (cos x))

series160.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (/ (- 1.0 (cos x)) x) x)
57.0ms	(/ (- 1.0 (cos x)) x)
39.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

174 → 174

Iterations

Iter	Nodes
done	5003
2	1582
1	604
0	259

prune748.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)) x))
0.4b	(+ 1.0 (cos x))
0.4b	(pow (cos x) 3)
1.0b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
144×	`prod-diff`
117×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `fma-def`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`pow-to-exp` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 304

Calls

4 calls:

100.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)) x))
10.0ms	(+ 1.0 (cos x))
3.0ms	(pow (cos x) 3)
34.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series375.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)) x))
11.0ms	(+ 1.0 (cos x))
49.0ms	(pow (cos x) 3)
70.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.9s

Counts

316 → 316

Iterations

Iter	Nodes
done	5032
2	2533
1	854
0	337

prune871.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes114.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch121.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.03649639588302253
10	-17239113253358.373	-4.96108325192681e-05	-0.031198749760063066

simplify10.0ms

Iterations

Iter	Nodes
done	39
1	39
0	33

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	1664×	body	2560	valid
505.0ms	1176×	body	1280	valid
417.0ms	1501×	body	640	valid
157.0ms	941×	body	320	valid
145.0ms	2244×	body	80	valid
58.0ms	474×	body	160	valid