Details

sample220.0ms

Algorithm

intervals

Results

91.0ms	101×	body	1280	valid
50.0ms	17×	body	2560	valid
33.0ms	60×	body	640	valid
13.0ms	33×	body	320	valid
4.0ms	36×	body	80	valid
2.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize24.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
3.1b	(sin (+ x eps))

rewrite168.0ms

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:

145.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

series118.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (sin (+ x eps)) (sin x))
38.0ms	(sin (+ x eps))

simplify1.3s

Counts

46 → 46

Iterations

Useful iterations: done (1.3s)

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

prune294.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite223.0ms

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:

67.0ms	(+ (+ x eps) x)
63.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
90.0ms	(cos (/ (+ (+ x eps) x) 2))

series180.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (+ x eps) x)
88.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

60 → 60

Iterations

Useful iterations: done (1.2s)

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

prune483.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ (+ eps 0) 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)))
3.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

54.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (+ (+ x eps) x) 2)))))
0.0ms	(log1p (expm1 (cos (/ (+ (+ x eps) x) 2))))
1.0ms	(expm1 (cos (/ (+ (+ x eps) x) 2)))
77.0ms	(cos (/ (+ (+ x eps) x) 2))

series381.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (+ (+ x eps) x) 2)))))
90.0ms	(log1p (expm1 (cos (/ (+ (+ x eps) x) 2))))
99.0ms	(expm1 (cos (/ (+ (+ x eps) x) 2)))
55.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.7s

Counts

63 → 63

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	98	974
1	220	826
2	713	722
3	3693	698
done	5000	643

prune536.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ (+ eps 0) 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
3.1b	(cos (/ (fma 2 x eps) 2))

rewrite95.0ms

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:

74.0ms	(* (sin (/ (+ eps 0) 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
4.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
6.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
7.0ms	(cos (/ (fma 2 x eps) 2))

series236.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin (/ (+ eps 0) 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
39.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
80.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
40.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.6s

Counts

105 → 105

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	124	1784
1	306	1414
2	1831	1252
done	5000	1247

prune717.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

regimes311.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch284.0ms

Steps

Iters	Range		Point
10	5.024206171497321e-19	2.8868360106527892e-08	1.3684517598693572e-08
10	-4.26929226401081	-4.5846337071089676e-10	-1.0771685445320532e-08

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	31	55
1	40	53
2	41	53
done	41	53

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.9s	3316×	body	1280	valid
1.6s	1824×	body	640	valid
1.2s	633×	body	2560	valid
247.0ms	762×	body	320	valid
173.0ms	1094×	body	80	valid
82.0ms	371×	body	160	valid