Details

sample150.0ms

Algorithm

intervals

Results

73.0ms	103×	body	1280	valid
26.0ms	19×	body	2560	valid
24.0ms	55×	body	640	valid
7.0ms	26×	body	320	valid
4.0ms	44×	body	80	valid
2.0ms	9×	body	160	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize16.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
3.4b	(sin (+ x eps))

rewrite105.0ms

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:

87.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

series74.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify4.5s

Counts

46 → 46

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	91	662
1	194	539
2	450	452
3	1388	388
4	4919	374
done	5000	374

prune147.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
0.2b	(/ (fma 2 x eps) 2)
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `sin-cos-mult` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

24.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
10.0ms	(/ (fma 2 x eps) 2)
5.0ms	(cos (/ (fma 2 x eps) 2))

series139.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
37.0ms	(/ (fma 2 x eps) 2)
28.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.3s

Counts

68 → 68

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	116	850
1	227	829
2	548	740
3	1189	738
4	2816	636
done	5000	636

prune260.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
0.2b	(/ (fma 2 x eps) 2)
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

22.0ms	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
5.0ms	(/ (fma 2 x eps) 2)
4.0ms	(cos (/ (fma 2 x eps) 2))

series194.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
43.0ms	(/ (fma 2 x eps) 2)
53.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.0s

Counts

67 → 67

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	110	829
1	215	807
2	535	716
3	1165	712
4	2732	616
done	5000	616

prune209.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cos (fma 1/2 eps x)) (sin (/ eps 2))))
3.4b	(cos (fma 1/2 eps x))
3.4b	(cos (fma 1/2 eps x))
3.4b	(cos (fma 1/2 eps x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

6.0ms	(cbrt (* (cos (fma 1/2 eps x)) (sin (/ eps 2))))
3.0ms	(cos (fma 1/2 eps x))
3.0ms	(cos (fma 1/2 eps x))
3.0ms	(cos (fma 1/2 eps x))

series178.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (* (cos (fma 1/2 eps x)) (sin (/ eps 2))))
27.0ms	(cos (fma 1/2 eps x))
21.0ms	(cos (fma 1/2 eps x))
22.0ms	(cos (fma 1/2 eps x))

simplify2.0s

Counts

53 → 53

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	61	544
1	115	538
2	213	486
3	516	470
4	1712	459
done	5001	454

prune200.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes77.0ms

Accuracy

99% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.1b

bsearch124.0ms

Steps

Iters	Range		Point
8	9.073269354155488e-21	1.3273336497419229e-17	1.3130033279220329e-17
9	-0.002338049553438653	-4.347782938444816e-12	-1.1565737311297234e-08

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	50
1	32	37
done	32	37

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.8s	3371×	body	1280	valid
762.0ms	611×	body	2560	valid
589.0ms	1842×	body	640	valid
179.0ms	720×	body	320	valid
76.0ms	1114×	body	80	valid
46.0ms	342×	body	160	valid