Details

sample189.0ms

Algorithm

intervals

Results

109.0ms	144×	body	1280	valid
31.0ms	21×	body	2560	valid
23.0ms	54×	body	640	valid
7.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid
1.0ms	6×	body	80	valid

simplify5.0ms

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: 42.6b

localize18.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite68.0ms

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:

50.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series106.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (cos (+ x eps)) (cos x))
37.0ms	(cos (+ x eps))

simplify875.0ms

Counts

46 → 46

Iterations

Useful iterations: done (872.0ms)

Iter	Nodes	Cost
0	91	664
1	202	543
2	726	453
done	5000	389

prune168.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

137.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
35.0ms	(+ (+ x eps) x)
139.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
72.0ms	(sin (/ (+ (+ x eps) x) 2))

series233.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
33.0ms	(+ (+ x eps) x)
69.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
40.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify995.0ms

Counts

84 → 84

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	129	1298
1	309	1154
2	1142	999
done	5001	966

prune431.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

45.0ms	(+ (+ x eps) x)
96.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
61.0ms	(sin (/ (+ (+ x eps) x) 2))

series191.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
122.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
44.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify933.0ms

Counts

59 → 59

Iterations

Useful iterations: done (932.0ms)

Iter	Nodes	Cost
0	99	751
1	248	725
2	1103	619
done	5001	597

prune282.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (+ (+ x eps) x) 2))))
0.3b	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (+ (+ x eps) x) 2)))))
0.4b	(log1p (sin (/ (+ (+ x eps) x) 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite119.0ms

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:

0.0ms	(expm1 (log1p (sin (/ (+ (+ x eps) x) 2))))
29.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (+ (+ x eps) x) 2)))))
1.0ms	(log1p (sin (/ (+ (+ x eps) x) 2)))
87.0ms	(sin (/ (+ (+ x eps) x) 2))

series375.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(expm1 (log1p (sin (/ (+ (+ x eps) x) 2))))
171.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (+ (+ x eps) x) 2)))))
77.0ms	(log1p (sin (/ (+ (+ x eps) x) 2)))
37.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

63 → 63

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	99	978
1	224	877
2	977	742
done	5001	718

prune246.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

regimes205.0ms

Accuracy

97.2% (0.4b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 14.9b

bsearch190.0ms

Steps

Iters	Range		Point
10	5.2366538615162886e-09	44039.89650146889	9.76354326473103e-05
8	-527.3133570883257	-0.03117879455470207	-0.03196418493759398

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	52
1	36	52
done	36	52

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.6s	4477×	body	1280	valid
1.6s	1831×	body	640	valid
991.0ms	647×	body	2560	valid
396.0ms	671×	body	320	valid
50.0ms	292×	body	160	valid
8.0ms	82×	body	80	valid