Details

sample71.0ms

Algorithm

intervals

Results

32.0ms	63×	body	1280	valid
15.0ms	57×	body	640	valid
7.0ms	22×	body	2560	valid
5.0ms	28×	body	320	valid
3.0ms	77×	body	80	valid
1.0ms	9×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) 1)
0.8b	(+ x (sqrt (+ (* x x) 1)))
2.4b	(log (+ x (sqrt (+ (* x x) 1))))
14.3b	(sqrt (+ (* x x) 1))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt`
5×	`add-exp-log`
4×	`log-prod` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`+-commutative` `log-div` `sum-log` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+ (* x x) 1)
16.0ms	(+ x (sqrt (+ (* x x) 1)))
16.0ms	(log (+ x (sqrt (+ (* x x) 1))))
9.0ms	(sqrt (+ (* x x) 1))

series282.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x x) 1)
53.0ms	(+ x (sqrt (+ (* x x) 1)))
150.0ms	(log (+ x (sqrt (+ (* x x) 1))))
40.0ms	(sqrt (+ (* x x) 1))

simplify1.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5004
3	2367
2	827
1	307
0	130

prune227.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.2b	(* -1/6 (* (* x x) x))
17.3b	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
23×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`associate-r`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt` `add-log-exp`
7×	`associate-l`
6×	`pow-plus` `pow-prod-up`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`pow2` `pow-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `associate-+l+` `flip3-+` `pow3` `pow-exp` `flip-+`

Counts

4 → 91

Calls

4 calls:

11.0ms	(* 3/40 (pow x 5))
19.0ms	(* (* x x) x)
49.0ms	(* -1/6 (* (* x x) x))
31.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 3/40 (pow x 5))
41.0ms	(* (* x x) x)
43.0ms	(* -1/6 (* (* x x) x))
62.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1177
1	344
0	132

prune310.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ -1/8 (* (* x x) x)) (+ (/ 1/2 x) x))
0.1b	(* (* x x) x)
0.3b	(/ -1/8 (* (* x x) x))
10.0b	(log (+ x (+ (/ -1/8 (* (* x x) x)) (+ (/ 1/2 x) x))))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
22×	`*-un-lft-identity`
19×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`add-sqr-sqrt` `distribute-lft-out` `add-log-exp`
8×	`add-cube-cbrt`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`insert-posit16`
3×	`cbrt-undiv` `sum-log` `flip3-+` `times-frac` `div-exp` `associate-r` `pow-prod-down` `flip-+` `associate-/l*`
2×	`pow2` `log-div` `frac-add` `pow-sqr`
1×	`+-commutative` `associate-+r+` `clear-num` `associate-/r` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

93.0ms	(+ (/ -1/8 (* (* x x) x)) (+ (/ 1/2 x) x))
22.0ms	(* (* x x) x)
17.0ms	(/ -1/8 (* (* x x) x))
242.0ms	(log (+ x (+ (/ -1/8 (* (* x x) x)) (+ (/ 1/2 x) x))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (/ -1/8 (* (* x x) x)) (+ (/ 1/2 x) x))
40.0ms	(* (* x x) x)
57.0ms	(/ -1/8 (* (* x x) x))
110.0ms	(log (+ x (+ (/ -1/8 (* (* x x) x)) (+ (/ 1/2 x) x))))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	1909
1	480
0	178

prune306.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1/16 (pow x 5))
0.3b	(/ 1/8 (* (* x x) x))
11.7b	(log (- (+ (/ 1/8 (* (* x x) x)) (/ -1/2 x)) (/ 1/16 (pow x 5))))
18.7b	(- (+ (/ 1/8 (* (* x x) x)) (/ -1/2 x)) (/ 1/16 (pow x 5)))

rewrite739.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`times-frac`
23×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`unpow-prod-down`
9×	`log-prod` `add-log-exp`
8×	`associate-/r*` `difference-of-squares`
6×	`div-exp` `frac-sub` `associate-/l*` `sqr-pow`
5×	`pow1` `log-div`
4×	`cbrt-undiv` `insert-posit16` `distribute-lft-out--`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `diff-log` `frac-add` `flip-+` `div-inv` `flip--` `distribute-lft-out`
1×	`pow-to-exp` `sum-log` `sub-neg` `rem-log-exp` `pow-exp` `associate--l+` `log-pow`

Counts

4 → 118

Calls

4 calls:

8.0ms	(/ 1/16 (pow x 5))
31.0ms	(/ 1/8 (* (* x x) x))
226.0ms	(log (- (+ (/ 1/8 (* (* x x) x)) (/ -1/2 x)) (/ 1/16 (pow x 5))))
469.0ms	(- (+ (/ 1/8 (* (* x x) x)) (/ -1/2 x)) (/ 1/16 (pow x 5)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1/16 (pow x 5))
59.0ms	(/ 1/8 (* (* x x) x))
135.0ms	(log (- (+ (/ 1/8 (* (* x x) x)) (/ -1/2 x)) (/ 1/16 (pow x 5))))
70.0ms	(- (+ (/ 1/8 (* (* x x) x)) (/ -1/2 x)) (/ 1/16 (pow x 5)))

simplify1.7s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
2	2118
1	588
0	265

prune569.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.8b

bsearch86.0ms

Steps

Iters	Range		Point
8	0.113095154289168	29.100869698027953	0.9612525386224373
7	-1.1375194732999505	-0.018988436667384805	-1.0681179944727555

simplify6.0ms

Iterations

Iter	Nodes
done	43
1	43
0	34

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.6s	2359×	body	1280	valid
972.0ms	1599×	body	640	valid
417.0ms	768×	body	2560	valid
183.0ms	812×	body	320	valid
145.0ms	2063×	body	80	valid
52.0ms	399×	body	160	valid