Details

sample101.0ms

Algorithm

intervals

Results

45.0ms	51×	body	2560	valid
17.0ms	35×	body	1280	valid
12.0ms	42×	body	640	valid
8.0ms	36×	body	320	valid
7.0ms	77×	body	80	valid
2.0ms	15×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	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: 29.4b

localize16.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
15.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

5.0ms	(- 1.0 (cos x))
17.0ms	(/ (- 1.0 (cos x)) (* x x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(- 1.0 (cos x))
72.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5074
3	2415
2	651
1	217
0	88

prune221.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.4b	(- 1.0 (cos x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

27.0ms	(/ (/ (- 1.0 (cos x)) x) x)
29.0ms	(/ (- 1.0 (cos x)) x)
12.0ms	(- 1.0 (cos x))

series138.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (/ (- 1.0 (cos x)) x) x)
59.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	1389
1	530
0	229

prune633.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `difference-cubes` `+-commutative` `sum-log` `sub-neg` `pow-pow` `distribute-lft-in` `flip3--` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

19.0ms	(* (cos x) (+ 1.0 (cos x)))
4.0ms	(pow (cos x) 3)
5.0ms	(+ 1.0 (cos x))
20.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series168.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos x) (+ 1.0 (cos x)))
33.0ms	(pow (cos x) 3)
11.0ms	(+ 1.0 (cos x))
72.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
2	1430
1	411
0	146

prune589.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.5b	(+ 1.0 (cos x))
1.2b	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))
1.3b	(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow1` `*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`log-prod` `log-pow`
4×	`exp-prod` `pow3`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`pow2` `+-commutative` `log-div` `sqr-cos` `sum-log` `flip3-+` `pow-plus` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
5.0ms	(+ 1.0 (cos x))
45.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))
88.0ms	(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cos x) (cos x))
11.0ms	(+ 1.0 (cos x))
57.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))
85.0ms	(log (exp (- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))))

simplify1.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5004
3	2977
2	1033
1	344
0	137

prune447.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes142.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.5b

bsearch91.0ms

Steps

Iters	Range		Point
8	0.0004390994911134099	0.778402845272117	0.029235651627996857
9	-0.1501579911863904	-8.136897775944376e-09	-0.031614486696612494

simplify15.0ms

Iterations

Iter	Nodes
done	60
1	60
0	45

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1552×	body	2560	valid
965.0ms	1275×	body	1280	valid
326.0ms	1411×	body	640	valid
224.0ms	2308×	body	80	valid
198.0ms	956×	body	320	valid
55.0ms	498×	body	160	valid