Details

sample184.0ms

Algorithm

intervals

Results

107.0ms	157×	body	1280	valid
27.0ms	17×	body	2560	valid
26.0ms	59×	body	640	valid
3.0ms	11×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	4×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	202
1	9	202
2	10	202
done	10	202

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize54.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
4.4b	(cos (+ x eps))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series94.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify3.4s

Counts

30 → 30

Iterations

Useful iterations: 5 (1.9s)

Iter	Nodes	Cost
0	65	8505
1	135	7661
2	280	7661
3	652	7581
4	1465	7542
5	4022	7502
done	5015	7502

prune190.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (* 1/2 eps))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ (+ x eps) x) 2)) (sin (* 1/2 eps)))
4.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
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:

91.0ms	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (* 1/2 eps))))
25.0ms	(+ (+ x eps) x)
99.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (* 1/2 eps)))
51.0ms	(sin (/ (+ (+ x eps) x) 2))

series343.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (* 1/2 eps))))
41.0ms	(+ (+ x eps) x)
129.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (* 1/2 eps)))
40.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify4.2s

Counts

72 → 72

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	116	23492
1	283	21915
2	883	21675
3	4310	21069
done	5002	20948

prune496.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* (sin (* 1/2 eps)) -2) (sin (+ (* 1/2 eps) x)))
4.3b	(sin (+ (* 1/2 eps) x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `sin-sum` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 28

Calls

2 calls:

52.0ms	(* (* (sin (* 1/2 eps)) -2) (sin (+ (* 1/2 eps) x)))
23.0ms	(sin (+ (* 1/2 eps) x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (* (sin (* 1/2 eps)) -2) (sin (+ (* 1/2 eps) x)))
30.0ms	(sin (+ (* 1/2 eps) x))

simplify3.2s

Counts

34 → 34

Iterations

Useful iterations: 3 (921.0ms)

Iter	Nodes	Cost
0	72	11056
1	188	10252
2	597	10252
3	1949	10052
done	5002	10052

prune307.0ms

Pruning

15 alts after pruning (15 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))
0.1b	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
0.2b	(* (cos (* 1/2 eps)) (sin x))
0.2b	(* (* (sin (* 1/2 eps)) -2) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

14.0ms	(* (sin (* 1/2 eps)) (cos x))
38.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
27.0ms	(* (cos (* 1/2 eps)) (sin x))
106.0ms	(* (* (sin (* 1/2 eps)) -2) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin (* 1/2 eps)) (cos x))
135.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
70.0ms	(* (cos (* 1/2 eps)) (sin x))
191.0ms	(* (* (sin (* 1/2 eps)) -2) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))))

simplify3.0s

Counts

82 → 82

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	154	32991
1	433	30770
2	1670	30649
done	5002	30489

prune529.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes398.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	484
1	20	484
done	20	484

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.1s	4415×	body	1280	valid
1.3s	1868×	body	640	valid
1.1s	675×	body	2560	valid
214.0ms	685×	body	320	valid
56.0ms	89×	body	80	valid
53.0ms	268×	body	160	valid