Details

sample164.0ms

Algorithm

intervals

Results

64.0ms	101×	body	1280	valid
46.0ms	24×	body	2560	valid
25.0ms	66×	body	640	valid
8.0ms	27×	body	320	valid
3.0ms	30×	body	80	valid
1.0ms	8×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize16.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

115.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify751.0ms

Counts

46 → 46

Iterations

Useful iterations: done (750.0ms)

Iter	Nodes	Cost
0	91	662
1	203	542
2	771	452
done	5000	388

prune121.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`fma-def` `distribute-lft-out`
3×	`expm1-log1p-u` `associate-r` `associate-l` `sum-log` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

59.0ms	(+ (+ x eps) x)
51.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
62.0ms	(cos (/ (+ (+ x eps) x) 2))

series154.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ x eps) x)
87.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
29.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify826.0ms

Counts

60 → 60

Iterations

Useful iterations: done (824.0ms)

Iter	Nodes	Cost
0	99	768
1	240	695
2	1026	617
done	5000	596

prune255.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (+ (+ x eps) x) 2)))))
0.3b	(log1p (expm1 (cos (/ (+ (+ x eps) x) 2))))
0.4b	(expm1 (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

27.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (+ (+ x eps) x) 2)))))
0.0ms	(log1p (expm1 (cos (/ (+ (+ x eps) x) 2))))
0.0ms	(expm1 (cos (/ (+ (+ x eps) x) 2)))
52.0ms	(cos (/ (+ (+ x eps) x) 2))

series270.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (+ (+ x eps) x) 2)))))
72.0ms	(log1p (expm1 (cos (/ (+ (+ x eps) x) 2))))
64.0ms	(expm1 (cos (/ (+ (+ x eps) x) 2)))
33.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

63 → 63

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	98	974
1	220	826
2	713	722
3	3693	698
done	5000	643

prune303.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.2b	(* (sin (/ (+ eps 0) 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
0.4b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

72.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
99.0ms	(* (sin (/ (+ eps 0) 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
112.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
52.0ms	(cos (/ (+ (+ x eps) x) 2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
55.0ms	(* (sin (/ (+ eps 0) 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
32.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
47.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.2s

Counts

81 → 81

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	117	1365
1	248	1168
2	878	1025
3	4336	1004
done	5000	1002

prune253.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

regimes135.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.6b

bsearch153.0ms

Steps

Iters	Range		Point
7	2.8927808134808724e-12	4.1843392194405927e-10	4.118793419307952e-10
11	-911936.9907706906	-2.4582005881584278e-17	-9.179827039913243e-09

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	31	55
1	40	53
2	41	53
done	41	53

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	3325×	body	1280	valid
794.0ms	654×	body	2560	valid
676.0ms	1850×	body	640	valid
242.0ms	765×	body	320	valid
88.0ms	335×	body	160	valid
76.0ms	1071×	body	80	valid