Details

sample179.0ms

Algorithm

intervals

Results

114.0ms	147×	body	1280	valid
25.0ms	20×	body	2560	valid
19.0ms	55×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize27.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ eps x)) (cos x))
2.4b	(cos (+ eps x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

23.0ms	(- (cos (+ eps x)) (cos x))
18.0ms	(cos (+ eps x))

series173.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(- (cos (+ eps x)) (cos x))
71.0ms	(cos (+ eps x))

simplify617.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1148
2	352
1	131
0	65

prune266.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(/ (+ (+ x eps) x) 2)
0.3b	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
2.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

31.0ms	(+ (+ x eps) x)
82.0ms	(/ (+ (+ x eps) x) 2)
109.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
67.0ms	(sin (/ (+ (+ x eps) x) 2))

series216.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (+ x eps) x)
41.0ms	(/ (+ (+ x eps) x) 2)
106.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
40.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify564.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1202
1	300
0	132

prune558.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
2.5b	(sin (/ (+ (+ x x) eps) 2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

3.0ms	(cbrt (sin (/ eps 2)))
4.0ms	(cbrt (sin (/ eps 2)))
4.0ms	(cbrt (sin (/ eps 2)))
51.0ms	(sin (/ (+ (+ x x) eps) 2))

series562.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt (sin (/ eps 2)))
152.0ms	(cbrt (sin (/ eps 2)))
163.0ms	(cbrt (sin (/ eps 2)))
58.0ms	(sin (/ (+ (+ x x) eps) 2))

simplify747.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	1375
2	312
1	122
0	60

prune418.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x x) eps) 2)))
2.5b	(sin (/ (+ (+ x x) eps) 2))
2.5b	(sin (/ (+ (+ x x) eps) 2))
2.5b	(sin (/ (+ (+ x x) eps) 2))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

32.0ms	(cbrt (sin (/ (+ (+ x x) eps) 2)))
50.0ms	(sin (/ (+ (+ x x) eps) 2))
39.0ms	(sin (/ (+ (+ x x) eps) 2))
39.0ms	(sin (/ (+ (+ x x) eps) 2))

series328.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (sin (/ (+ (+ x x) eps) 2)))
59.0ms	(sin (/ (+ (+ x x) eps) 2))
54.0ms	(sin (/ (+ (+ x x) eps) 2))
53.0ms	(sin (/ (+ (+ x x) eps) 2))

simplify746.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
3	1159
2	318
1	119
0	57

prune381.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes483.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch224.0ms

Steps

Iters	Range		Point
10	7.42116589675916e-09	160.65039477392645	0.00014597753908590782
9	-3322970397.4786234	-6367.3348759504115	-6443.306290177518

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.5s	4435×	body	1280	valid
998.0ms	637×	body	2560	valid
852.0ms	1874×	body	640	valid
614.0ms	665×	body	320	valid
54.0ms	307×	body	160	valid
8.0ms	82×	body	80	valid