Details

sample195.0ms

Algorithm

intervals

Results

100.0ms	101×	body	1280	valid
38.0ms	28×	body	2560	valid
32.0ms	55×	body	640	valid
11.0ms	33×	body	320	valid
3.0ms	30×	body	80	valid
2.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
4.4b	(sin (+ x eps))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

75.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series90.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify1.3s

Counts

48 → 48

Iterations

Iter	Nodes
4	3120
3	1109
2	432
1	203
0	92

prune373.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ eps x))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
4.3b	(cos (/ (+ x (+ eps x)) 2))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `sum-log` `fma-def` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

20.0ms	(+ x (+ eps x))
29.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
38.0ms	(cos (/ (+ x (+ eps x)) 2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ x (+ eps x))
56.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
43.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify649.0ms

Counts

62 → 62

Iterations

Iter	Nodes
3	2082
2	678
1	235
0	100

prune554.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
0.3b	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.4b	(expm1 (cos (/ (+ x (+ eps x)) 2)))
4.3b	(cos (/ (+ x (+ eps x)) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

10.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
0.0ms	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
0.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
22.0ms	(cos (/ (+ x (+ eps x)) 2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (+ x (+ eps x)) 2)))))
79.0ms	(log1p (expm1 (cos (/ (+ x (+ eps x)) 2))))
58.0ms	(expm1 (cos (/ (+ x (+ eps x)) 2)))
34.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.4s

Counts

67 → 67

Iterations

Iter	Nodes
4	2300
3	1027
2	469
1	216
0	100

prune772.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
0.3b	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))
0.3b	(log1p (cos (/ (+ x (+ eps x)) 2)))
4.3b	(cos (/ (+ x (+ eps x)) 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

0.0ms	(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
19.0ms	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))
1.0ms	(log1p (cos (/ (+ x (+ eps x)) 2)))
20.0ms	(cos (/ (+ x (+ eps x)) 2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
105.0ms	(* (sin (/ eps 2)) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))))
62.0ms	(log1p (cos (/ (+ x (+ eps x)) 2)))
26.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.6s

Counts

67 → 67

Iterations

Iter	Nodes
5	3532
4	1973
3	947
2	427
1	198
0	96

prune547.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes136.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.3b

bsearch184.0ms

Steps

Iters	Range		Point
9	5.0298683109421105e-11	0.0006943122548678707	1.136872105742304e-08
9	-6.606666156357114e-05	-3.708178749948539e-10	-7.256929432906464e-09

simplify7.0ms

Iterations

Iter	Nodes
2	37
1	37
0	27

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.3s	3293×	body	1280	valid
1.2s	1758×	body	640	valid
863.0ms	660×	body	2560	valid
266.0ms	808×	body	320	valid
171.0ms	1111×	body	80	valid
70.0ms	370×	body	160	valid