Details

sample172.0ms

Algorithm

intervals

Results

93.0ms	76×	body	1280	valid
32.0ms	50×	body	640	valid
13.0ms	15×	body	2560	valid
10.0ms	24×	body	320	valid
7.0ms	71×	body	80	valid
5.0ms	20×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize24.0ms

Local error

Found 3 expressions with local error:

1.6b	(+ x (sqrt (+ (* x x) 1)))
3.8b	(log (+ x (sqrt (+ (* x x) 1))))
14.0b	(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:

23.0ms	(+ x (sqrt (+ (* x x) 1)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series252.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ x (sqrt (+ (* x x) 1)))
157.0ms	(log (+ x (sqrt (+ (* x x) 1))))
33.0ms	(sqrt (+ (* x x) 1))

simplify1.4s

Counts

54 → 54

Iterations

Iter	Nodes
done	2000
4	2000
3	1978
2	707
1	273
0	121

prune486.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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))
17.2b	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

rewrite164.0ms

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:

17.0ms	(* 3/40 (pow x 5))
31.0ms	(* (* x x) x)
77.0ms	(* -1/6 (* (* x x) x))
38.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* 3/40 (pow x 5))
64.0ms	(* (* x x) x)
52.0ms	(* -1/6 (* (* x x) x))
85.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

simplify1.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	2020
3	2020
2	1177
1	344
0	132

prune877.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
0.1b	(* (* x x) x)
0.2b	(/ 1/8 (* (* x x) x))
10.7b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

19.0ms	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
14.0ms	(* (* x x) x)
14.0ms	(/ 1/8 (* (* x x) x))
162.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
35.0ms	(* (* x x) x)
42.0ms	(/ 1/8 (* (* x x) x))
92.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify955.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2002
3	2002
2	1462
1	421
0	170

prune714.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(/ 1/8 (* (* x x) x))
12.4b	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
18.8b	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`add-exp-log`
18×	`*-un-lft-identity` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
8×	`frac-add` `add-cube-cbrt`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `distribute-lft-out`
5×	`log-div` `log-prod`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`cbrt-undiv` `sum-log` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `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 → 92

Calls

4 calls:

19.0ms	(* (* x x) x)
15.0ms	(/ 1/8 (* (* x x) x))
74.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
90.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x x) x)
46.0ms	(/ 1/8 (* (* x x) x))
122.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
67.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

simplify1.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	2001
3	2001
2	1987
1	526
0	189

prune834.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes62.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.2b

bsearch130.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.9645338519110289
9	-24078.920296370652	-0.35383103211093586	-1.061520745717705

simplify8.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	2354×	body	1280	valid
787.0ms	1532×	body	640	valid
575.0ms	784×	body	2560	valid
247.0ms	784×	body	320	valid
180.0ms	2135×	body	80	valid
70.0ms	411×	body	160	valid