Details

sample173.0ms

Algorithm

intervals

Results

73.0ms	97×	body	1280	valid
40.0ms	26×	body	2560	valid
29.0ms	62×	body	640	valid
8.0ms	26×	body	320	valid
4.0ms	38×	body	80	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize18.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite115.0ms

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:

103.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series97.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (sin (+ x eps)) (sin x))
43.0ms	(sin (+ x eps))

simplify924.0ms

Counts

46 → 46

Iterations

Useful iterations: done (922.0ms)

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

prune166.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite118.0ms

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:

34.0ms	(+ (+ x eps) x)
30.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
52.0ms	(cos (/ (+ (+ x eps) x) 2))

series129.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ x eps) x)
65.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
27.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify873.0ms

Counts

60 → 60

Iterations

Useful iterations: done (869.0ms)

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

prune336.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))
2.9b	(cos (fma 1/2 eps x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

21.0ms	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))
3.0ms	(cos (fma 1/2 eps x))

series74.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* (sin (* 1/2 eps)) (cos (fma 1/2 eps x)))
26.0ms	(cos (fma 1/2 eps x))

simplify2.7s

Counts

37 → 37

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	67	442
1	143	436
2	469	388
3	2985	377
done	5000	372

prune267.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 1/2 eps)) (cos x))
0.1b	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
0.2b	(* (sin (* 1/2 eps)) (sin x))
0.2b	(* (sin (* 1/2 eps)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`fma-neg` `diff-log`

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (cos (* 1/2 eps)) (cos x))
34.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
23.0ms	(* (sin (* 1/2 eps)) (sin x))
127.0ms	(* (sin (* 1/2 eps)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos (* 1/2 eps)) (cos x))
96.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
56.0ms	(* (sin (* 1/2 eps)) (sin x))
141.0ms	(* (sin (* 1/2 eps)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	154	1847
1	370	1781
2	1616	1627
done	5000	1575

prune600.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	20	22
2	24	22
3	25	22
done	25	22

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.9s	3237×	body	1280	valid
1.2s	635×	body	2560	valid
1.2s	1841×	body	640	valid
214.0ms	801×	body	320	valid
155.0ms	1135×	body	80	valid
64.0ms	351×	body	160	valid