Details

sample153.0ms

Algorithm

intervals

Results

61.0ms	63×	body	2560	valid
27.0ms	41×	body	1280	valid
24.0ms	74×	body	80	valid
21.0ms	46×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	15×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.9b	(- 1 (cos x))
19.2b	(/ (- 1 (cos x)) (* x x))

rewrite37.0ms

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:

16.0ms	(- 1 (cos x))
20.0ms	(/ (- 1 (cos x)) (* x x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- 1 (cos x))
87.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.1s

Counts

53 → 53

Iterations

Iter	Nodes
done	5021
3	3531
2	777
1	230
0	93

prune189.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.2b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
18.9b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite63.0ms

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))
28.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series174.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
29.0ms	(* (sin x) (sin x))
19.0ms	(+ 1 (cos x))
82.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify2.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	2002
1	507
0	182

prune453.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

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))
10.0ms	(/ (sin x) x)
11.0ms	(/ (tan (/ x 2)) x)

series272.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
41.0ms	(/ (sin x) x)
98.0ms	(/ (tan (/ x 2)) x)

simplify1.9s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1577
1	448
0	166

prune493.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (/ (sin x) 1) (/ (* x x) (tan (/ x 2))))
18.1b	(/ (* x x) (tan (/ x 2)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

230×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
37×	`add-exp-log`
28×	`add-cbrt-cube`
25×	`div-inv`
23×	`div-exp`
16×	`associate-/r/`
15×	`cbrt-undiv` `tan-quot`
14×	`associate-/l*`
11×	`associate-/r*`
4×	`prod-exp`
3×	`1-exp` `cbrt-unprod`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 176

Calls

2 calls:

16.0ms	(/ (/ (sin x) 1) (/ (* x x) (tan (/ x 2))))
17.0ms	(/ (* x x) (tan (/ x 2)))

series236.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(/ (/ (sin x) 1) (/ (* x x) (tan (/ x 2))))
106.0ms	(/ (* x x) (tan (/ x 2)))

simplify1.7s

Counts

182 → 182

Iterations

Iter	Nodes
done	5019
2	3280
1	1030
0	350

prune773.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes48.0ms

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
done	9
1	9
0	8

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	1584×	body	2560	valid
880.0ms	1210×	body	1280	valid
741.0ms	1487×	body	640	valid
351.0ms	910×	body	320	valid
264.0ms	2328×	body	80	valid
98.0ms	481×	body	160	valid