Details

sample131.0ms

Algorithm

intervals

Results

59.0ms	69×	body	1280	valid
29.0ms	52×	body	640	valid
17.0ms	26×	body	2560	valid
10.0ms	29×	body	320	valid
6.0ms	69×	body	80	valid
2.0ms	11×	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: 52.8b

localize13.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1)))
2.8b	(log (+ x (sqrt (+ (* x x) 1))))
14.9b	(sqrt (+ (* x x) 1))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

12.0ms	(+ x (sqrt (+ (* x x) 1)))
23.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series244.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(+ x (sqrt (+ (* x x) 1)))
140.0ms	(log (+ x (sqrt (+ (* x x) 1))))
36.0ms	(sqrt (+ (* x x) 1))

simplify920.0ms

Counts

54 → 54

Iterations

Iter	Nodes
done	2000
3	1978
2	707
1	273
0	121

prune204.0ms

Pruning

3 alts after pruning (3 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)
0.1b	(* -1/6 (* (* x x) x))
17.6b	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

rewrite89.0ms

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:

8.0ms	(* 3/40 (pow x 5))
15.0ms	(* (* x x) x)
36.0ms	(* -1/6 (* (* x x) x))
28.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 3/40 (pow x 5))
54.0ms	(* (* x x) x)
62.0ms	(* -1/6 (* (* x x) x))
85.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

simplify600.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	2007
2	1177
1	344
0	132

prune302.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.1b	(* -1/6 (* (* x x) x))
17.6b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (pow x 5)))

rewrite100.0ms

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`
7×	`associate-l`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `pow-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `flip3-+` `pow3` `pow-exp` `flip-+`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* 3/40 (pow x 5))
16.0ms	(* (* x x) x)
34.0ms	(* -1/6 (* (* x x) x))
35.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (pow x 5)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* 3/40 (pow x 5))
53.0ms	(* (* x x) x)
54.0ms	(* -1/6 (* (* x x) x))
208.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (pow x 5)))

simplify559.0ms

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
2	1065
1	332
0	124

prune307.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ 1/8 (* (* x x) x))
10.9b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

19.0ms	(* (* x x) x)
20.0ms	(/ 1/8 (* (* x x) x))
169.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series182.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (* x x) x)
40.0ms	(/ 1/8 (* (* x x) x))
92.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify600.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	2000
2	942
1	312
0	135

prune234.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.3b

bsearch143.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	0.9619268999163055
10	-121993772661.31783	-0.0015977726548224043	-1.0757153356474918

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.1s	2390×	body	1280	valid
697.0ms	1524×	body	640	valid
438.0ms	801×	body	2560	valid
224.0ms	736×	body	320	valid
212.0ms	2141×	body	80	valid
66.0ms	408×	body	160	valid