Details

sample184.0ms

Algorithm

intervals

Results

110.0ms	113×	body	1280	valid
27.0ms	20×	body	2560	valid
20.0ms	54×	body	640	valid
7.0ms	26×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	28×	body	80	valid

simplify9.0ms

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: 37.1b

localize10.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ x eps))

rewrite76.0ms

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:

64.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify852.0ms

Counts

46 → 46

Iterations

Useful iterations: done (850.0ms)

Iter	Nodes	Cost
0	91	662
1	203	542
2	771	452
done	5000	388

prune126.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite144.0ms

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` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

46.0ms	(+ (+ x eps) x)
33.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
63.0ms	(cos (/ (+ (+ x eps) x) 2))

series139.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (+ x eps) x)
72.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
38.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify890.0ms

Counts

60 → 60

Iterations

Useful iterations: done (888.0ms)

Iter	Nodes	Cost
0	99	768
1	240	695
2	1026	617
done	5000	596

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ eps x))
0.3b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ eps x)) 2)))
4.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

18.0ms	(+ x (+ eps x))
34.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ eps x)) 2)))
70.0ms	(cos (/ (+ x (+ eps x)) 2))

series133.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ x (+ eps x))
69.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ x (+ eps x)) 2)))
36.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify933.0ms

Counts

59 → 59

Iterations

Useful iterations: done (931.0ms)

Iter	Nodes	Cost
0	99	768
1	243	693
2	1051	615
done	5001	596

prune283.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ (+ eps 0) 2)) (cbrt (pow (cos (/ (+ x (+ eps x)) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ x (+ eps x)) 2)) 3))
0.5b	(pow (cos (/ (+ x (+ eps x)) 2)) 3)
4.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

64.0ms	(* (sin (/ (+ eps 0) 2)) (cbrt (pow (cos (/ (+ x (+ eps x)) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ x (+ eps x)) 2)) 3))
7.0ms	(pow (cos (/ (+ x (+ eps x)) 2)) 3)
35.0ms	(cos (/ (+ x (+ eps x)) 2))

series233.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin (/ (+ eps 0) 2)) (cbrt (pow (cos (/ (+ x (+ eps x)) 2)) 3)))
44.0ms	(cbrt (pow (cos (/ (+ x (+ eps x)) 2)) 3))
83.0ms	(pow (cos (/ (+ x (+ eps x)) 2)) 3)
26.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.1s

Counts

105 → 105

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	127	1921
1	320	1540
2	1881	1356
done	5002	1337

prune337.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.4b

regimes158.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.5b

bsearch196.0ms

Steps

Iters	Range		Point
9	5.841499356922819e-12	0.0004268116563047139	1.7444808358242096e-08
9	-8.253445947576724e-07	-1.3572074081350282e-15	-1.1066748065615766e-08

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	29	53
1	38	51
2	39	51
done	39	51

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.9s	3296×	body	1280	valid
1.2s	1883×	body	640	valid
1.0s	609×	body	2560	valid
222.0ms	762×	body	320	valid
151.0ms	1092×	body	80	valid
67.0ms	358×	body	160	valid