Details

sample229.0ms

Algorithm

intervals

Results

130.0ms	129×	body	1280	valid
40.0ms	25×	body	2560	valid
36.0ms	69×	body	640	valid
7.0ms	18×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize27.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
1.9b	(cos (+ x eps))

rewrite43.0ms

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` `insert-posit16`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

11.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series90.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

simplify2.5s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	3787
4	1424
3	658
2	282
1	137
0	67

prune163.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
1.8b	(sin (/ (+ x (+ x eps)) 2))

rewrite166.0ms

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` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

58.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
16.0ms	(+ x (+ x eps))
71.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
20.0ms	(sin (/ (+ x (+ x eps)) 2))

series302.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
43.0ms	(+ x (+ x eps))
109.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
35.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5043
3	3226
2	832
1	289
0	121

prune445.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
2.0b	(sin (+ (/ eps 2) x))

rewrite75.0ms

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×	`insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 30

Calls

2 calls:

48.0ms	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
26.0ms	(sin (+ (/ eps 2) x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
37.0ms	(sin (+ (/ eps 2) x))

simplify2.2s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	1849
2	538
1	193
0	76

prune232.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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`
4×	`insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `sin-cos-mult`

Counts

4 → 74

Calls

4 calls:

16.0ms	(+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x)))
12.0ms	(* (sin (/ eps 2)) (cos x))
13.0ms	(* (cos (/ eps 2)) (sin x))
53.0ms	(* (* -2 (sin (/ eps 2))) (+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x)))
89.0ms	(* (sin (/ eps 2)) (cos x))
85.0ms	(* (cos (/ eps 2)) (sin x))
219.0ms	(* (* -2 (sin (/ eps 2))) (+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x))))

simplify2.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5002
2	1540
1	443
0	161

prune527.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes212.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.1s	4444×	body	1280	valid
1.3s	1831×	body	640	valid
1.2s	610×	body	2560	valid
382.0ms	737×	body	320	valid
73.0ms	281×	body	160	valid
12.0ms	97×	body	80	valid