Details

sample101.0ms

Algorithm

intervals

Results

37.0ms	42×	body	2560	valid
19.0ms	40×	body	1280	valid
16.0ms	54×	body	640	valid
8.0ms	34×	body	320	valid
6.0ms	67×	body	80	valid
3.0ms	19×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize21.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
12.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite28.0ms

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))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- 1.0 (cos x))
74.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune239.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

13.0ms	(/ (sqrt (- 1.0 (cos x))) x)
91.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
5.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (sqrt (- 1.0 (cos x))) x)
76.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
32.0ms	(- 1.0 (cos x))
34.0ms	(- 1.0 (cos x))

simplify957.0ms

Counts

218 → 218

Iterations

Iter	Nodes
done	5000
1	737
0	231

prune862.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.2b	(/ (- 1.0 (cos x)) x)
1.2b	(- 1.0 (cos x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-l`
17×	`add-cbrt-cube`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

3 → 115

Calls

3 calls:

36.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
25.0ms	(/ (- 1.0 (cos x)) x)
10.0ms	(- 1.0 (cos x))

series194.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
82.0ms	(/ (- 1.0 (cos x)) x)
35.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	2726
1	551
0	189

prune450.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.3b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

13.0ms	(* (cos x) (cos x))
5.0ms	(+ 1.0 (cos x))
5.0ms	(- 1.0 (cos x))
7.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (cos x) (cos x))
11.0ms	(+ 1.0 (cos x))
21.0ms	(- 1.0 (cos x))
55.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	2011
1	320
0	121

prune478.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes103.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch94.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.033817197098290584
10	-17239113253358.373	-4.96108325192681e-05	-0.031198749760063066

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	1664×	body	2560	valid
724.0ms	1176×	body	1280	valid
398.0ms	1501×	body	640	valid
149.0ms	941×	body	320	valid
133.0ms	2244×	body	80	valid
53.0ms	474×	body	160	valid