Details

sample44.0ms

Algorithm

intervals

Results

13.0ms	55×	body	640	valid
7.0ms	126×	body	80	valid
6.0ms	38×	body	320	valid
6.0ms	20×	body	1280	valid
2.0ms	17×	body	160	valid

simplify979.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	88	15
5	135	15
6	162	15
7	211	15
8	441	15
9	1208	15
done	5000	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

14.0ms	(/ 1.0 (- x 1.0))
21.0ms	(/ 1.0 (+ x 1.0))
82.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
396.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
30.0ms	(/ 1.0 (+ x 1.0))
61.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
271.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.1s

Counts

126 → 126

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	213	1832
1	516	1716
2	1963	1630
done	5000	1624

prune369.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (pow x 7))
0.2b	(/ 2.0 (pow x 5))
0.4b	(/ 2.0 (pow x 3))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
26×	`associate-/r*`
18×	`add-exp-log`
12×	`cube-prod` `sqr-pow`
9×	`div-exp` `add-cbrt-cube` `associate-/l*`
4×	`cube-mult` `unpow3`
3×	`pow1` `cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `add-log-exp`

Counts

3 → 155

Calls

3 calls:

20.0ms	(/ 2.0 (pow x 7))
11.0ms	(/ 2.0 (pow x 5))
14.0ms	(/ 2.0 (pow x 3))

series200.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ 2.0 (pow x 7))
65.0ms	(/ 2.0 (pow x 5))
52.0ms	(/ 2.0 (pow x 3))

simplify1.0s

Counts

164 → 164

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	228	1740
1	451	1506
2	2108	1462
done	5001	1460

prune716.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (pow x 7))
0.1b	(* (/ 1 (* x x)) (/ 2.0 x))
0.2b	(/ 2.0 (pow x 5))
0.3b	(/ 1 (* x x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
64×	`times-frac`
60×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`add-cbrt-cube`
25×	`div-exp`
24×	`unpow-prod-down`
23×	`prod-exp`
15×	`associate-/r*`
14×	`pow1`
13×	`associate-r`
11×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
8×	`sqr-pow`
7×	`associate-l`
6×	`rec-exp` `pow-flip` `1-exp` `unswap-sqr`
5×	`div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-to-exp` `pow-prod-down` `pow-exp`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `inv-pow`

Counts

4 → 180

Calls

4 calls:

13.0ms	(/ 2.0 (pow x 7))
73.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
15.0ms	(/ 2.0 (pow x 5))
25.0ms	(/ 1 (* x x))

series233.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 2.0 (pow x 7))
63.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
66.0ms	(/ 2.0 (pow x 5))
22.0ms	(/ 1 (* x x))

simplify3.6s

Counts

192 → 192

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	269	2053
1	703	1820
2	4713	1585
done	5000	1585

prune749.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 2.0 (* x x)) (cbrt (pow x 3)))
0.2b	(/ 2.0 (pow x 5))
0.3b	(/ 2.0 (* x x))
41.2b	(cbrt (pow x 3))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
108×	`cbrt-prod`
89×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down`
27×	`cube-prod`
23×	`add-exp-log` `associate-/r*`
19×	`div-inv`
17×	`add-cbrt-cube`
13×	`associate-/l*` `sqr-pow`
10×	`div-exp`
9×	`cube-mult` `unpow3`
8×	`cbrt-undiv`
4×	`pow1` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-to-exp` `pow1/3` `pow-exp` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 231

Calls

4 calls:

29.0ms	(/ (/ 2.0 (* x x)) (cbrt (pow x 3)))
10.0ms	(/ 2.0 (pow x 5))
9.0ms	(/ 2.0 (* x x))
3.0ms	(cbrt (pow x 3))

series186.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (/ 2.0 (* x x)) (cbrt (pow x 3)))
59.0ms	(/ 2.0 (pow x 5))
40.0ms	(/ 2.0 (* x x))
20.0ms	(cbrt (pow x 3))

simplify518.0ms

Counts

243 → 243

Iterations

Useful iterations: done (503.0ms)

Iter	Nodes	Cost
0	313	3635
1	753	2785
done	5001	2667

prune936.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes139.0ms

Accuracy

98.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.6b

bsearch144.0ms

Steps

Iters	Range		Point
9	0.00015484893005477947	28918.939680702064	117.99697548641551
10	-2676750800.736259	-2.9526231381329305e-09	-104.34266919097254

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	61
1	42	61
done	42	61

end0.0ms

sample2.1s

Algorithm

intervals

Results

996.0ms	1919×	body	640	valid
302.0ms	956×	body	320	valid
289.0ms	4124×	body	80	valid
216.0ms	540×	body	1280	valid
54.0ms	463×	body	160	valid