Details

sample149.0ms

Algorithm

intervals

Results

74.0ms	135×	body	1280	valid
29.0ms	24×	body	2560	valid
22.0ms	61×	body	640	valid
7.0ms	26×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	80	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

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize12.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.4b	(cos (+ x eps))

rewrite40.0ms

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:

28.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series124.0ms

Counts

2 → 6

Calls

2 calls:

104.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

simplify924.0ms

Counts

46 → 46

Iterations

Useful iterations: done (922.0ms)

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

prune204.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.0b	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
0.2b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
3.5b	(sin (/ (+ (+ x eps) x) 2))

rewrite383.0ms

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:

32.0ms	(+ (+ x eps) x)
161.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
135.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (+ x eps) x)
83.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
63.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify866.0ms

Counts

84 → 84

Iterations

Useful iterations: done (863.0ms)

Iter	Nodes	Cost
0	129	1298
1	310	1158
2	1149	999
done	5001	966

prune378.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (* (sin (fma 1/2 eps x)) -2))
3.5b	(sin (fma 1/2 eps x))

rewrite62.0ms

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:

56.0ms	(* (sin (* 1/2 eps)) (* (sin (fma 1/2 eps x)) -2))
5.0ms	(sin (fma 1/2 eps x))

series141.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(* (sin (* 1/2 eps)) (* (sin (fma 1/2 eps x)) -2))
45.0ms	(sin (fma 1/2 eps x))

simplify2.0s

Counts

36 → 36

Iterations

Useful iterations: 3 (904.0ms)

Iter	Nodes	Cost
0	70	479
1	156	466
2	564	394
3	2571	389
done	5001	389

prune146.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
0.1b	(* (cos (* 1/2 eps)) (sin x))
0.1b	(* (sin (* 1/2 eps)) (cos x))
0.2b	(* (sin (* 1/2 eps)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

35.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
32.0ms	(* (cos (* 1/2 eps)) (sin x))
22.0ms	(* (sin (* 1/2 eps)) (cos x))
216.0ms	(* (sin (* 1/2 eps)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))

series407.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
69.0ms	(* (cos (* 1/2 eps)) (sin x))
53.0ms	(* (sin (* 1/2 eps)) (cos x))
173.0ms	(* (sin (* 1/2 eps)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	155	1555
1	404	1450
2	1958	1277
done	5001	1275

prune391.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

0% (0.3b 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	16	24
1	22	24
done	22	24

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.9s	4454×	body	1280	valid
1.4s	654×	body	2560	valid
711.0ms	1856×	body	640	valid
283.0ms	685×	body	320	valid
55.0ms	271×	body	160	valid
8.0ms	80×	body	80	valid