Details

sample129.0ms

Algorithm

intervals

Results

70.0ms	143×	body	1280	valid
22.0ms	20×	body	2560	valid
16.0ms	56×	body	640	valid
5.0ms	24×	body	320	valid
2.0ms	11×	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

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite50.0ms

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:

29.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series131.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(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

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize43.0ms

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)))
4.1b	(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:

126.0ms	(* -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)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))

series266.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
43.0ms	(+ (+ x eps) x)
98.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify841.0ms

Counts

84 → 84

Iterations

Useful iterations: done (839.0ms)

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

prune327.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (sin (/ (+ (+ x eps) x) 2))))
0.3b	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (sin (/ (+ (+ x eps) x) 2)))))
0.4b	(log1p (sin (/ (+ (+ x eps) x) 2)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite132.0ms

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:

0.0ms	(expm1 (log1p (sin (/ (+ (+ x eps) x) 2))))
46.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (sin (/ (+ (+ x eps) x) 2)))))
1.0ms	(log1p (sin (/ (+ (+ x eps) x) 2)))
84.0ms	(sin (/ (+ (+ x eps) x) 2))

series346.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(expm1 (log1p (sin (/ (+ (+ x eps) x) 2))))
144.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (sin (/ (+ (+ x eps) x) 2)))))
92.0ms	(log1p (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.4s

Counts

63 → 63

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	94	962
1	194	821
2	652	715
3	3105	693
done	5001	639

prune432.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
4.2b	(sin (fma 1/2 eps x))

rewrite68.0ms

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:

62.0ms	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
5.0ms	(sin (fma 1/2 eps x))

series101.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
26.0ms	(sin (fma 1/2 eps x))

simplify1.6s

Counts

36 → 36

Iterations

Useful iterations: 3 (661.0ms)

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

prune139.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes199.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.3s	4426×	body	1280	valid
1.5s	609×	body	2560	valid
872.0ms	1880×	body	640	valid
221.0ms	697×	body	320	valid
54.0ms	312×	body	160	valid
7.0ms	76×	body	80	valid