Details

sample128.0ms

Algorithm

intervals

Results

43.0ms	48×	body	2560	valid
37.0ms	49×	body	640	valid
20.0ms	35×	body	1280	valid
8.0ms	30×	body	320	valid
7.0ms	81×	body	80	valid
2.0ms	13×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	30
4	30
3	28
2	23
1	15
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize12.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1 (cos x))
14.4b	(/ (- 1 (cos x)) (* x x))

rewrite22.0ms

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))
16.0ms	(/ (- 1 (cos x)) (* x x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- 1 (cos x))
75.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.2s

Counts

53 → 53

Iterations

Iter	Nodes
done	5139
3	3004
2	707
1	230
0	93

prune235.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
14.2b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite60.0ms

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)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
26.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
15.0ms	(+ 1 (cos x))
97.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5012
2	1801
1	507
0	182

prune488.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

15.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
6.0ms	(/ (tan (/ x 2)) x)
8.0ms	(/ (sin x) x)

series237.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
87.0ms	(/ (tan (/ x 2)) x)
41.0ms	(/ (sin x) x)

simplify1.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1539
1	448
0	166

prune494.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

66.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
8.0ms	(/ (sin x) x)
15.0ms	(* (cos (* 1/2 x)) x)
30.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
34.0ms	(/ (sin x) x)
76.0ms	(* (cos (* 1/2 x)) x)
63.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))

simplify1.7s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1899
1	477
0	184

prune610.0ms

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
done	13
1	13
0	10

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.0s	1607×	body	2560	valid
916.0ms	1250×	body	1280	valid
717.0ms	1473×	body	640	valid
329.0ms	990×	body	320	valid
305.0ms	2188×	body	80	valid
143.0ms	492×	body	160	valid