Details

sample216.0ms

Algorithm

intervals

Results

92.0ms	126×	body	1280	valid
52.0ms	63×	body	640	valid
40.0ms	24×	body	2560	valid
14.0ms	31×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

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: 38.3b

localize10.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
6.4b	(cos (+ x eps))

rewrite30.0ms

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` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

17.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series127.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (cos (+ x eps)) (cos x))
39.0ms	(cos (+ x eps))

simplify5.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.1s)

Iter	Nodes	Cost
0	91	664
1	194	540
2	439	453
3	1358	389
4	4783	375
done	5000	375

prune166.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.2b	(sin (/ (fma 2 x eps) 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

52.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
40.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
5.0ms	(sin (/ (fma 2 x eps) 2))

series219.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
71.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
56.0ms	(sin (/ (fma 2 x eps) 2))

simplify7.0s

Counts

60 → 60

Iterations

Useful iterations: 4 (4.5s)

Iter	Nodes	Cost
0	101	959
1	221	944
2	620	803
3	1792	799
4	3798	786
done	5000	786

prune247.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (fma eps 1/2 x)) (* -2 (sin (* 1/2 eps))))
6.2b	(sin (fma eps 1/2 x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

54.0ms	(* (sin (fma eps 1/2 x)) (* -2 (sin (* 1/2 eps))))
5.0ms	(sin (fma eps 1/2 x))

series120.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (sin (fma eps 1/2 x)) (* -2 (sin (* 1/2 eps))))
39.0ms	(sin (fma eps 1/2 x))

simplify9.2s

Counts

36 → 36

Iterations

Useful iterations: 3 (495.0ms)

Iter	Nodes	Cost
0	71	476
1	157	463
2	460	391
3	1407	386
4	2768	386
5	4935	386
done	5000	386

prune184.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
0.1b	(* (sin (* eps 1/2)) (cos x))
0.1b	(* (cos (* eps 1/2)) (sin x))
0.3b	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (* -2 (sin (* 1/2 eps))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

61.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
32.0ms	(* (sin (* eps 1/2)) (cos x))
20.0ms	(* (cos (* eps 1/2)) (sin x))
182.0ms	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (* -2 (sin (* 1/2 eps))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
79.0ms	(* (sin (* eps 1/2)) (cos x))
80.0ms	(* (cos (* eps 1/2)) (sin x))
228.0ms	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (* -2 (sin (* 1/2 eps))))

simplify2.3s

Counts

89 → 89

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	161	1552
1	393	1447
2	1310	1275
done	5000	1268

prune504.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes225.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	35
1	25	35
done	25	35

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.5s	4423×	body	1280	valid
1.8s	1822×	body	640	valid
1.0s	640×	body	2560	valid
243.0ms	738×	body	320	valid
57.0ms	299×	body	160	valid
8.0ms	78×	body	80	valid