Details

sample164.0ms

Algorithm

intervals

Results

70.0ms	137×	body	1280	valid
40.0ms	60×	body	640	valid
32.0ms	26×	body	2560	valid
6.0ms	25×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	2×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize13.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ 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` `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:

31.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

series94.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify906.0ms

Counts

46 → 46

Iterations

Useful iterations: done (904.0ms)

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

prune223.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

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)))
3.2b	(sin (/ (+ (+ x eps) x) 2))

rewrite413.0ms

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:

143.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
59.0ms	(+ (+ x eps) x)
143.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
66.0ms	(sin (/ (+ (+ x eps) x) 2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
43.0ms	(+ (+ x eps) x)
92.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify980.0ms

Counts

84 → 84

Iterations

Useful iterations: done (978.0ms)

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

prune655.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (+ (+ x eps) x) 2)))
0.2b	(log1p (expm1 (sin (/ (+ (+ x eps) x) 2))))
0.3b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (sin (/ (+ (+ x eps) x) 2)))))
3.2b	(sin (/ (+ (+ x eps) x) 2))

rewrite114.0ms

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:

1.0ms	(expm1 (sin (/ (+ (+ x eps) x) 2)))
1.0ms	(log1p (expm1 (sin (/ (+ (+ x eps) x) 2))))
54.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (sin (/ (+ (+ x eps) x) 2)))))
57.0ms	(sin (/ (+ (+ x eps) x) 2))

series378.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(expm1 (sin (/ (+ (+ x eps) x) 2)))
91.0ms	(log1p (expm1 (sin (/ (+ (+ x eps) x) 2))))
160.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (sin (/ (+ (+ x eps) x) 2)))))
35.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.0s

Counts

63 → 63

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	94	962
1	197	816
2	650	715
3	3274	694
done	5000	638

prune568.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
3.2b	(sin (fma 1/2 eps x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`sin-sum` `associate-r` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

48.0ms	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
6.0ms	(sin (fma 1/2 eps x))

series140.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
44.0ms	(sin (fma 1/2 eps x))

simplify1.9s

Counts

36 → 36

Iterations

Useful iterations: 3 (786.0ms)

Iter	Nodes	Cost
0	69	479
1	153	466
2	541	394
3	2335	389
done	5000	389

prune154.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes405.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	20	22
done	20	22

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.0s	4428×	body	1280	valid
1.4s	635×	body	2560	valid
748.0ms	1893×	body	640	valid
187.0ms	662×	body	320	valid
57.0ms	301×	body	160	valid
7.0ms	81×	body	80	valid