Details

sample139.0ms

Algorithm

intervals

Results

52.0ms	303×	body	80	nan
24.0ms	49×	body	1280	valid
14.0ms	179×	body	80	valid
10.0ms	30×	body	640	valid
5.0ms	7×	body	2560	valid
4.0ms	17×	body	320	valid
0.0ms	2×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	86
6	86
5	84
4	78
3	67
2	50
1	32
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.2b	(/ a (* b 3.0))
25.2b	(cos (- y (/ (* z t) 3.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r` `div-exp` `insert-posit16` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`cos-sum` `clear-num` `frac-2neg` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 76

Calls

4 calls:

10.0ms	(/ (* z t) 3.0)
31.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
7.0ms	(/ a (* b 3.0))
15.0ms	(cos (- y (/ (* z t) 3.0)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* z t) 3.0)
101.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
22.0ms	(/ a (* b 3.0))
38.0ms	(cos (- y (/ (* z t) 3.0)))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
2	1368
1	425
0	174

prune687.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
28.5b	(cos (/ (* z t) 3.0))
28.8b	(sin (/ (* z t) 3.0))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`times-frac` `associate-r` `pow-prod-down` `associate-r/` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult`

Counts

4 → 62

Calls

4 calls:

7.0ms	(/ a (* b 3.0))
58.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
5.0ms	(cos (/ (* z t) 3.0))
5.0ms	(sin (/ (* z t) 3.0))

series351.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ a (* b 3.0))
288.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
14.0ms	(cos (/ (* z t) 3.0))
21.0ms	(sin (/ (* z t) 3.0))

simplify1.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1616
1	451
0	166

prune704.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 16.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.3333333333333333 (* z t))
0.2b	(/ a (* b 3.0))
28.7b	(cos (* 0.3333333333333333 (* z t)))
28.8b	(sin (/ (* z t) 3.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`times-frac` `associate-l` `pow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `div-inv`

Counts

4 → 57

Calls

4 calls:

16.0ms	(* 0.3333333333333333 (* z t))
7.0ms	(/ a (* b 3.0))
24.0ms	(cos (* 0.3333333333333333 (* z t)))
3.0ms	(sin (/ (* z t) 3.0))

series95.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 0.3333333333333333 (* z t))
31.0ms	(/ a (* b 3.0))
15.0ms	(cos (* 0.3333333333333333 (* z t)))
22.0ms	(sin (/ (* z t) 3.0))

simplify3.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	1978
2	633
1	225
0	108

prune732.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 16.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
1.0b	(* (cbrt 0.3333333333333333) (cbrt 0.3333333333333333))
28.4b	(cos (* (* (cbrt 0.3333333333333333) (cbrt 0.3333333333333333)) (* (cbrt 0.3333333333333333) (* z t))))
28.8b	(sin (/ (* z t) 3.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`cbrt-prod`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `-commutative` `div-inv`

Counts

4 → 79

Calls

4 calls:

7.0ms	(/ a (* b 3.0))
10.0ms	(* (cbrt 0.3333333333333333) (cbrt 0.3333333333333333))
55.0ms	(cos (* (* (cbrt 0.3333333333333333) (cbrt 0.3333333333333333)) (* (cbrt 0.3333333333333333) (* z t))))
4.0ms	(sin (/ (* z t) 3.0))

series117.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(/ a (* b 3.0))
0.0ms	(* (cbrt 0.3333333333333333) (cbrt 0.3333333333333333))
73.0ms	(cos (* (* (cbrt 0.3333333333333333) (cbrt 0.3333333333333333)) (* (cbrt 0.3333333333333333) (* z t))))
18.0ms	(sin (/ (* z t) 3.0))

simplify3.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5003
4	4607
3	1677
2	593
1	229
0	119

prune637.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 16.2b

regimes4.8s

Accuracy

52.4% (1.9b remaining)

Error of 17.4b against oracle of 15.5b and baseline of 19.5b

bsearch3.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	58
1	58
0	43

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.7s	9051×	body	80	nan
1.5s	1569×	body	1280	valid
1.3s	5637×	body	80	valid
523.0ms	926×	body	640	valid
371.0ms	361×	body	2560	valid
227.0ms	434×	body	320	valid
120.0ms	205×	body	160	valid