Details

sample97.0ms

Algorithm

intervals

Results

43.0ms	93×	body	1280	valid
22.0ms	24×	body	2560	valid
15.0ms	60×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	18×	body	160	valid
2.0ms	39×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(sin (+ x eps))
2.5b	(- (sin (+ x eps)) (sin x))

rewrite31.0ms

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:

4.0ms	(sin (+ x eps))
26.0ms	(- (sin (+ x eps)) (sin x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(sin (+ x eps))
46.0ms	(- (sin (+ x eps)) (sin x))

simplify1.3s

Counts

46 → 46

Iterations

Useful iterations: 3 (267.0ms)

Iter	Nodes	Cost
0	91	662
1	198	539
2	551	452
3	2284	388
done	5000	388

prune98.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ (+ 0 eps) 2)))
2.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite56.0ms

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` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

15.0ms	(+ (+ x eps) x)
13.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ (+ 0 eps) 2)))
27.0ms	(cos (/ (+ (+ x eps) x) 2))

series119.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (+ x eps) x)
73.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ (+ 0 eps) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.6s

Counts

59 → 59

Iterations

Useful iterations: 3 (316.0ms)

Iter	Nodes	Cost
0	94	741
1	234	671
2	730	589
3	3004	525
done	5000	525

prune213.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (fma x 2 eps) 2)))
2.0b	(cos (/ (+ (+ x eps) x) 2))
2.0b	(cos (/ (+ (+ x eps) x) 2))
2.0b	(cos (/ (fma x 2 eps) 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (cos (/ (fma x 2 eps) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))
26.0ms	(cos (/ (+ (+ x eps) x) 2))
2.0ms	(cos (/ (fma x 2 eps) 2))

series160.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (cos (/ (fma x 2 eps) 2)))
24.0ms	(cos (/ (+ (+ x eps) x) 2))
26.0ms	(cos (/ (+ (+ x eps) x) 2))
24.0ms	(cos (/ (fma x 2 eps) 2))

simplify2.4s

Counts

52 → 52

Iterations

Useful iterations: 4 (419.0ms)

Iter	Nodes	Cost
0	60	591
1	110	576
2	222	506
3	679	479
4	2990	371
done	5000	371

prune271.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (cos (fma eps 1/2 x)))
2.0b	(cos (fma eps 1/2 x))
2.0b	(cos (/ (+ (+ x eps) x) 2))
2.0b	(cos (/ (fma x 2 eps) 2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
1×	`cos-sum` `expm1-log1p` `fma-udef` `expm1-udef`

Counts

4 → 39

Calls

4 calls:

0.0ms	(expm1 (cos (fma eps 1/2 x)))
1.0ms	(cos (fma eps 1/2 x))
21.0ms	(cos (/ (+ (+ x eps) x) 2))
2.0ms	(cos (/ (fma x 2 eps) 2))

series119.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(expm1 (cos (fma eps 1/2 x)))
19.0ms	(cos (fma eps 1/2 x))
22.0ms	(cos (/ (+ (+ x eps) x) 2))
27.0ms	(cos (/ (fma x 2 eps) 2))

simplify2.8s

Counts

51 → 51

Iterations

Useful iterations: 4 (481.0ms)

Iter	Nodes	Cost
0	84	494
1	156	479
2	326	423
3	912	408
4	3541	357
done	5000	357

prune267.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

regimes123.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.0b

bsearch87.0ms

Steps

Iters	Range		Point
7	6.841021425788069e-10	8.116859208030337e-08	7.436477518387171e-09
6	-2.8343233054530806e-08	-2.2450763006537216e-09	-6.6823151206119754e-09

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	53
1	38	51
2	42	51
done	42	51

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3253×	body	1280	valid
584.0ms	649×	body	2560	valid
473.0ms	1841×	body	640	valid
135.0ms	779×	body	320	valid
66.0ms	1072×	body	80	valid
44.0ms	406×	body	160	valid