Details

sample180.0ms

Algorithm

intervals

Results

119.0ms	149×	body	1280	valid
21.0ms	56×	body	640	valid
14.0ms	11×	body	2560	valid
7.0ms	22×	body	320	valid
3.0ms	16×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite47.0ms

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

series125.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(- (cos (+ x eps)) (cos x))
63.0ms	(cos (+ x eps))

simplify862.0ms

Counts

46 → 46

Iterations

Useful iterations: done (861.0ms)

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

prune167.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

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)
0.2b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
3.8b	(sin (/ (+ (+ x eps) x) 2))

rewrite399.0ms

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:

139.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
49.0ms	(+ (+ x eps) x)
152.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
55.0ms	(sin (/ (+ (+ x eps) x) 2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
41.0ms	(+ (+ x eps) x)
103.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
66.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify850.0ms

Counts

84 → 84

Iterations

Useful iterations: done (848.0ms)

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

prune411.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
3.9b	(sin (fma 1/2 eps x))

rewrite73.0ms

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:

68.0ms	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
3.0ms	(sin (fma 1/2 eps x))

series135.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(* (sin (fma 1/2 eps x)) (* (sin (* 1/2 eps)) -2))
40.0ms	(sin (fma 1/2 eps x))

simplify1.8s

Counts

36 → 36

Iterations

Useful iterations: 3 (741.0ms)

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

prune202.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

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

rewrite281.0ms

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-*l/` `flip-+` `unswap-sqr`
1×	`+-commutative` `fma-def` `sum-log` `sin-cos-mult`

Counts

4 → 77

Calls

4 calls:

55.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
40.0ms	(* (cos (* 1/2 eps)) (sin x))
40.0ms	(* (sin (* 1/2 eps)) (cos x))
141.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (* (sin (* 1/2 eps)) -2))

series542.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
76.0ms	(* (cos (* 1/2 eps)) (sin x))
74.0ms	(* (sin (* 1/2 eps)) (cos x))
253.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (* (sin (* 1/2 eps)) -2))

simplify1.6s

Counts

89 → 89

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	153	1555
1	393	1450
2	1812	1278
done	5001	1274

prune385.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes190.0ms

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	13	21
1	17	21
done	17	21

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.3s	4510×	body	1280	valid
1.9s	648×	body	2560	valid
920.0ms	1805×	body	640	valid
341.0ms	674×	body	320	valid
115.0ms	278×	body	160	valid
8.0ms	85×	body	80	valid