Details

sample140.0ms

Algorithm

intervals

Results

72.0ms	149×	body	1280	valid
24.0ms	18×	body	2560	valid
22.0ms	56×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid
0.0ms	1×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite49.0ms

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:

28.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

series112.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify5.0s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.0s)

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

prune142.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

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)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite69.0ms

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:

33.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
30.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
4.0ms	(sin (/ (fma 2 x eps) 2))

series249.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
103.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
50.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.4s

Counts

60 → 60

Iterations

Useful iterations: 4 (4.1s)

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

prune254.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

48.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
4.0ms	(sin (/ (fma 2 x eps) 2))

series145.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
49.0ms	(sin (/ (fma 2 x eps) 2))

simplify7.3s

Counts

35 → 35

Iterations

Useful iterations: 4 (4.2s)

Iter	Nodes	Cost
0	73	552
1	170	539
2	527	447
3	1627	444
4	3483	436
done	5000	436

prune151.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
0.3b	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
0.4b	(log1p (sin (/ (fma 2 x eps) 2)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

1.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
48.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
1.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
12.0ms	(sin (/ (fma 2 x eps) 2))

series403.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
164.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
82.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
42.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.8s

Counts

63 → 63

Iterations

Useful iterations: 4 (4.0s)

Iter	Nodes	Cost
0	98	906
1	205	811
2	585	688
3	1673	681
4	3448	665
done	5000	665

prune299.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes313.0ms

Accuracy

95.4% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 15.0b

bsearch102.0ms

Steps

Iters	Range		Point
5	526447839.8444867	1173724448.4928873	531195561.4738419
6	-1.6640733670284383e-05	-3.4900073017642136e-06	-1.1233368844796593e-05

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	26	50
1	32	38
done	32	38

end1.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	4421×	body	1280	valid
827.0ms	673×	body	2560	valid
603.0ms	1889×	body	640	valid
142.0ms	662×	body	320	valid
58.0ms	280×	body	160	valid
6.0ms	75×	body	80	valid