Details

sample208.0ms

Algorithm

intervals

Results

112.0ms	126×	body	1280	valid
38.0ms	24×	body	2560	valid
27.0ms	63×	body	640	valid
10.0ms	31×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize11.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
6.4b	(cos (+ x eps))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

17.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

series121.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (cos (+ x eps)) (cos x))
45.0ms	(cos (+ x eps))

simplify3.1s

Counts

30 → 30

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	65	311
1	192	299
2	875	279
done	5000	275

prune182.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

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)))
6.2b	(sin (/ (+ (+ x eps) x) 2))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

116.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
40.0ms	(+ (+ x eps) x)
164.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
50.0ms	(sin (/ (+ (+ x eps) x) 2))

series228.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
25.0ms	(+ (+ x eps) x)
85.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
40.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify990.0ms

Counts

72 → 72

Iterations

Useful iterations: done (988.0ms)

Iter	Nodes	Cost
0	121	1200
1	549	1081
done	5000	919

prune336.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
0.3b	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
6.2b	(sin (* 1/2 (+ (* 2 x) eps)))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`add-log-exp`
2×	`sin-sum` `*-commutative` `sin-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

138.0ms	(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
98.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
44.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

series338.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))
147.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
43.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

simplify3.8s

Counts

56 → 56

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	101	1005
1	403	981
done	5000	821

prune248.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps))) (* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2))))
0.1b	(* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2)))
0.1b	(* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps)))
0.3b	(* (+ (* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps))) (* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2)))) (sin (* 1/2 eps)))

rewrite544.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `sum-log` `sin-cos-mult`

Counts

4 → 68

Calls

4 calls:

131.0ms	(+ (* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps))) (* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2))))
73.0ms	(* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2)))
71.0ms	(* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps)))
265.0ms	(* (+ (* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps))) (* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2)))) (sin (* 1/2 eps)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ (* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps))) (* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2))))
80.0ms	(* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2)))
78.0ms	(* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps)))
220.0ms	(* (+ (* (sin (* 1/2 (* 2 x))) (cos (* 1/2 eps))) (* (cos (* (* 2 x) 1/2)) (sin (* eps 1/2)))) (sin (* 1/2 eps)))

simplify1.4s

Counts

80 → 80

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	150	1923
1	675	1853
done	5000	1645

prune447.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	78
1	29	78
done	29	78

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.7s	4423×	body	1280	valid
1.5s	640×	body	2560	valid
861.0ms	1822×	body	640	valid
247.0ms	738×	body	320	valid
62.0ms	299×	body	160	valid
7.0ms	78×	body	80	valid