Details

sample139.0ms

Algorithm

intervals

Results

51.0ms	57×	body	2560	valid
42.0ms	43×	body	1280	valid
19.0ms	39×	body	640	valid
8.0ms	27×	body	320	valid
8.0ms	77×	body	80	valid
3.0ms	13×	body	160	valid

simplify17.0ms

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: 32.4b

localize12.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1 (cos x))
17.1b	(/ (- 1 (cos x)) (* x x))

rewrite23.0ms

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:

5.0ms	(- 1 (cos x))
17.0ms	(/ (- 1 (cos x)) (* x x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1 (cos x))
78.0ms	(/ (- 1 (cos x)) (* x x))

simplify5.2s

Counts

53 → 53

Iterations

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

prune348.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))
16.9b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite62.0ms

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:

16.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
15.0ms	(* (sin x) (sin x))
6.0ms	(+ 1 (cos x))
24.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series152.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
19.0ms	(* (sin x) (sin x))
12.0ms	(+ 1 (cos x))
78.0ms	(/ (/ (* (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

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 90

Calls

3 calls:

18.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
8.0ms	(/ (sin x) x)
21.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series222.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
36.0ms	(/ (sin x) x)
96.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify7.8s

Counts

99 → 99

Iterations

Iter	Nodes
3	6327
2	1304
1	371
0	154

prune803.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

22.0ms	(/ (* (/ (sin x) x) (sin (/ x 2))) (* x (cos (/ x 2))))
7.0ms	(* x (cos (/ x 2)))
8.0ms	(/ (sin x) x)
16.0ms	(* (/ (sin x) x) (sin (/ x 2)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (* (/ (sin x) x) (sin (/ x 2))) (* x (cos (/ x 2))))
50.0ms	(* x (cos (/ x 2)))
55.0ms	(/ (sin x) x)
96.0ms	(* (/ (sin x) x) (sin (/ x 2)))

simplify531.0ms

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

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	11
1	11
0	10

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.7s	1585×	body	2560	valid
1.2s	1510×	body	640	valid
893.0ms	1279×	body	1280	valid
769.0ms	925×	body	320	valid
228.0ms	2254×	body	80	valid
127.0ms	447×	body	160	valid