Details

sample86.0ms

Algorithm

intervals

Results

42.0ms	57×	body	2560	valid
13.0ms	44×	body	1280	valid
12.0ms	56×	body	640	valid
4.0ms	28×	body	320	valid
4.0ms	57×	body	80	valid
1.0ms	14×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize24.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1 (cos x))
17.7b	(/ (- 1 (cos x)) (* x x))

rewrite49.0ms

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:

19.0ms	(- 1 (cos x))
28.0ms	(/ (- 1 (cos x)) (* x x))

series98.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- 1 (cos x))
62.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.0s

Counts

53 → 53

Iterations

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

prune169.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.2b	(* (sin x) (sin x))
0.5b	(+ 1 (cos x))
17.6b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite107.0ms

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:

39.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
6.0ms	(+ 1 (cos x))
35.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series199.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
19.0ms	(* (sin x) (sin x))
13.0ms	(+ 1 (cos x))
107.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5012
2	1801
1	507
0	182

prune471.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ 1 (cos x)) (* (/ x (sin x)) (/ x (sin x))))
0.1b	(* (/ x (sin x)) (/ x (sin x)))
0.5b	(/ 1 (* (+ 1 (cos x)) (* (/ x (sin x)) (/ x (sin x)))))
0.5b	(+ 1 (cos x))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-exp-log`
59×	`add-cbrt-cube`
48×	`add-sqr-sqrt`
43×	`times-frac`
40×	`prod-exp`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`div-exp`
22×	`pow1` `cbrt-unprod`
19×	`frac-times`
18×	`cbrt-undiv`
17×	`associate-l`
14×	`associate-r`
13×	`swap-sqr` `associate-*r/`
11×	`associate-*l/` `associate-/r/`
9×	`flip3-+` `flip-+`
7×	`pow-prod-down`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`div-inv` `unswap-sqr`
4×	`insert-posit16`
3×	`pow-flip` `associate-/l*`
2×	`*-commutative` `distribute-lft-out`
1×	`pow2` `+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 176

Calls

4 calls:

87.0ms	(* (+ 1 (cos x)) (* (/ x (sin x)) (/ x (sin x))))
50.0ms	(* (/ x (sin x)) (/ x (sin x)))
147.0ms	(/ 1 (* (+ 1 (cos x)) (* (/ x (sin x)) (/ x (sin x)))))
12.0ms	(+ 1 (cos x))

series305.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (+ 1 (cos x)) (* (/ x (sin x)) (/ x (sin x))))
101.0ms	(* (/ x (sin x)) (/ x (sin x)))
88.0ms	(/ 1 (* (+ 1 (cos x)) (* (/ x (sin x)) (/ x (sin x)))))
12.0ms	(+ 1 (cos x))

simplify1.9s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
2	2480
1	785
0	261

prune503.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt (/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x)))
17.6b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
17.6b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
17.6b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

68×	`times-frac`
67×	`add-cbrt-cube` `add-exp-log`
33×	`*-un-lft-identity`
30×	`cbrt-undiv` `div-exp` `associate-/l*`
19×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`prod-exp` `cbrt-unprod`
14×	`cbrt-prod` `associate-/r/`
11×	`div-inv`
7×	`flip3-+` `flip-+` `distribute-lft-out`
6×	`div-sub`
4×	`pow1` `insert-posit16` `add-log-exp`
3×	`clear-num` `associate-/r*` `frac-2neg` `sqr-sin` `associate-/l/`
1×	`cbrt-div` `pow1/3`

Counts

4 → 162

Calls

4 calls:

19.0ms	(cbrt (/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x)))
51.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
48.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
46.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series491.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x)))
85.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
101.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
84.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.4s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	1838
1	479
0	181

prune973.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes53.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	1604×	body	2560	valid
840.0ms	1239×	body	1280	valid
445.0ms	1505×	body	640	valid
189.0ms	931×	body	320	valid
173.0ms	2254×	body	80	valid
55.0ms	467×	body	160	valid