Details

sample205.0ms

Algorithm

intervals

Results

109.0ms	113×	body	1280	valid
33.0ms	21×	body	2560	valid
29.0ms	54×	body	640	valid
8.0ms	26×	body	320	valid
3.0ms	12×	body	160	valid
3.0ms	30×	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: 41.6b

localize10.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite96.0ms

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:

83.0ms	(- (sin (+ x eps)) (sin x))
12.0ms	(sin (+ x eps))

series100.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

simplify975.0ms

Counts

46 → 46

Iterations

Useful iterations: done (973.0ms)

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

prune141.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite152.0ms

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:

54.0ms	(+ (+ x eps) x)
49.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
46.0ms	(cos (/ (+ (+ x eps) x) 2))

series168.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (+ x eps) x)
87.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify768.0ms

Counts

60 → 60

Iterations

Useful iterations: done (766.0ms)

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

prune282.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (cos (/ (+ (+ x eps) x) 2))))
0.3b	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (+ (+ x eps) x) 2)))))
0.5b	(log1p (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`log1p-expm1-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:

1.0ms	(expm1 (log1p (cos (/ (+ (+ x eps) x) 2))))
48.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (+ (+ x eps) x) 2)))))
1.0ms	(log1p (cos (/ (+ (+ x eps) x) 2)))
55.0ms	(cos (/ (+ (+ x eps) x) 2))

series308.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(expm1 (log1p (cos (/ (+ (+ x eps) x) 2))))
112.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (+ (+ x eps) x) 2)))))
86.0ms	(log1p (cos (/ (+ (+ x eps) x) 2)))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

63 → 63

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	94	969
1	204	821
2	671	713
3	3288	693
done	5000	639

prune470.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite31.0ms

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:

26.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series319.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
102.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
63.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
36.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.7s

Counts

63 → 63

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	95	903
1	206	763
2	669	669
3	3425	661
done	5000	642

prune335.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

regimes199.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 14.9b

bsearch184.0ms

Steps

Iters	Range		Point
9	1.3016113514811783e-15	5.2366538615162886e-09	5.156835808069301e-09
8	-0.03117879455470207	-2.7237372521413145e-05	-2.7541666583250866e-05

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	55
1	40	40
2	41	40
done	41	40

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.4s	3317×	body	1280	valid
1.5s	1861×	body	640	valid
831.0ms	647×	body	2560	valid
197.0ms	1080×	body	80	valid
195.0ms	734×	body	320	valid
72.0ms	361×	body	160	valid