Details

sample223.0ms

Algorithm

intervals

Results

103.0ms	143×	body	1280	valid
33.0ms	28×	body	320	valid
32.0ms	21×	body	2560	valid
23.0ms	46×	body	640	valid
3.0ms	13×	body	160	valid
1.0ms	5×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize61.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite113.0ms

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:

66.0ms	(- (cos (+ x eps)) (cos x))
45.0ms	(cos (+ x eps))

series140.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(- (cos (+ x eps)) (cos x))
42.0ms	(cos (+ x eps))

simplify7.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
5	3910
4	1422
3	645
2	280
1	136
0	67

prune510.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize126.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ eps x))
0.2b	(/ (+ x (+ eps x)) 2)
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
3.4b	(sin (/ (+ x (+ eps x)) 2))

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

37.0ms	(+ x (+ eps x))
165.0ms	(/ (+ x (+ eps x)) 2)
199.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
121.0ms	(sin (/ (+ x (+ eps x)) 2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ x (+ eps x))
50.0ms	(/ (+ x (+ eps x)) 2)
112.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
59.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify7.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
3	3453
2	925
1	301
0	136

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize110.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (+ x (* eps 1/2))) (sin (* eps 1/2))))
0.3b	(* (sin (+ x (* eps 1/2))) (sin (* eps 1/2)))
3.4b	(sin (+ x (* eps 1/2)))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`insert-posit16` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`sin-sum` `associate-*r/` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

175.0ms	(* -2 (* (sin (+ x (* eps 1/2))) (sin (* eps 1/2))))
106.0ms	(* (sin (+ x (* eps 1/2))) (sin (* eps 1/2)))
27.0ms	(sin (+ x (* eps 1/2)))

series379.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(* -2 (* (sin (+ x (* eps 1/2))) (sin (* eps 1/2))))
150.0ms	(* (sin (+ x (* eps 1/2))) (sin (* eps 1/2)))
49.0ms	(sin (+ x (* eps 1/2)))

simplify5.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	2599
2	698
1	228
0	98

prune904.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize148.0ms

Local error

Found 4 expressions with local error:

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

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`insert-posit16`
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 → 72

Calls

4 calls:

108.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
44.0ms	(* (cos x) (sin (* eps 1/2)))
54.0ms	(* (sin x) (cos (* eps 1/2)))
276.0ms	(* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (sin (* eps 1/2)))

series847.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
118.0ms	(* (cos x) (sin (* eps 1/2)))
110.0ms	(* (sin x) (cos (* eps 1/2)))
404.0ms	(* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (sin (* eps 1/2)))

simplify4.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1452
1	356
0	145

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes980.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	24
1	24
0	17

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.4s	4357×	body	1280	valid
1.4s	1935×	body	640	valid
1.0s	617×	body	2560	valid
288.0ms	707×	body	320	valid
106.0ms	294×	body	160	valid
11.0ms	90×	body	80	valid