Details

sample141.0ms

Algorithm

intervals

Results

43.0ms	49×	body	2560	valid
34.0ms	30×	body	320	valid
23.0ms	35×	body	1280	valid
20.0ms	46×	body	640	valid
7.0ms	73×	body	80	valid
5.0ms	23×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	28
4	28
3	26
2	21
1	13
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize11.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1 (cos x))
13.7b	(/ (- 1 (cos x)) (* x x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 47

Calls

2 calls:

6.0ms	(- 1 (cos x))
20.0ms	(/ (- 1 (cos x)) (* x x))

series97.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1 (cos x))
76.0ms	(/ (- 1 (cos x)) (* x x))

simplify5.6s

Counts

53 → 53

Iterations

Iter	Nodes
4	5731
3	1877
2	652
1	223
0	93

prune425.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
13.8b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity`
22×	`times-frac`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`flip3-+` `flip-+` `insert-posit16` `div-inv`
3×	`div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

17.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
33.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series194.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
30.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
90.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify6.6s

Counts

127 → 127

Iterations

Iter	Nodes
3	9290
2	1817
1	494
0	182

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) x)
0.2b	(* (/ 1 x) (* (/ (sin x) x) (tan (/ x 2))))
0.2b	(* (/ (sin x) x) (tan (/ x 2)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
31×	`add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
22×	`prod-exp`
12×	`div-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv`
6×	`frac-times` `tan-quot` `associate-*r/`
4×	`associate-r` `pow-prod-down` `associate-*l/`
3×	`rec-exp` `associate-/r` `1-exp` `insert-posit16` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg`

Counts

3 → 113

Calls

3 calls:

16.0ms	(/ (sin x) x)
61.0ms	(* (/ 1 x) (* (/ (sin x) x) (tan (/ x 2))))
22.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series307.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (sin x) x)
141.0ms	(* (/ 1 x) (* (/ (sin x) x) (tan (/ x 2))))
131.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify19.2s

Counts

122 → 122

Iterations

Iter	Nodes
3	7924
2	1701
1	519
0	194

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ (sin x) x) (sin (/ x 2))) (* x (cos (/ x 2))))
0.1b	(/ (sin x) x)
0.1b	(* x (cos (/ x 2)))
0.2b	(* (/ (sin x) x) (sin (/ x 2)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
16×	`associate-l`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`pow1`
6×	`associate-r`
4×	`associate-/r` `insert-posit16` `associate-/l` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative`
1×	`associate-/l/`

Counts

4 → 107

Calls

4 calls:

33.0ms	(/ (* (/ (sin x) x) (sin (/ x 2))) (* x (cos (/ x 2))))
8.0ms	(/ (sin x) x)
8.0ms	(* x (cos (/ x 2)))
15.0ms	(* (/ (sin x) x) (sin (/ x 2)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (* (/ (sin x) x) (sin (/ x 2))) (* x (cos (/ x 2))))
51.0ms	(/ (sin x) x)
55.0ms	(* x (cos (/ x 2)))
78.0ms	(* (/ (sin x) x) (sin (/ x 2)))

simplify615.0ms

Counts

119 → 119

Iterations

Iter	Nodes
2	2017
1	456
0	183

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	10

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	1559×	body	2560	valid
1.1s	1511×	body	640	valid
906.0ms	1309×	body	1280	valid
366.0ms	934×	body	320	valid
256.0ms	2228×	body	80	valid
169.0ms	459×	body	160	valid