Details

sample91.0ms

Algorithm

intervals

Results

49.0ms	78×	body	1280	valid
17.0ms	48×	body	640	valid
7.0ms	31×	body	320	valid
6.0ms	15×	body	2560	valid
3.0ms	70×	body	80	valid
2.0ms	14×	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: 52.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1)))
4.0b	(log (+ x (sqrt (+ (* x x) 1))))
12.8b	(sqrt (+ (* x x) 1))

rewrite56.0ms

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:

17.0ms	(+ x (sqrt (+ (* x x) 1)))
17.0ms	(log (+ x (sqrt (+ (* x x) 1))))
21.0ms	(sqrt (+ (* x x) 1))

series255.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(+ x (sqrt (+ (* x x) 1)))
153.0ms	(log (+ x (sqrt (+ (* x x) 1))))
33.0ms	(sqrt (+ (* x x) 1))

simplify1.5s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	1978
2	707
1	273
0	121

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

19.0ms	(* 3/40 (pow x 5))
31.0ms	(* (* x x) x)
95.0ms	(* (* (* x x) x) 1/6)
27.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* 3/40 (pow x 5))
58.0ms	(* (* x x) x)
62.0ms	(* (* (* x x) x) 1/6)
92.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

simplify2.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
3	3928
2	964
1	330
0	134

prune287.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

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))
12.4b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite439.0ms

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:

34.0ms	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
33.0ms	(* (* x x) x)
37.0ms	(/ 1/8 (* (* x x) x))
331.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
48.0ms	(* (* x x) x)
77.0ms	(/ 1/8 (* (* x x) x))
162.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1462
1	421
0	170

prune328.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1/16 (pow x 5))
0.2b	(/ 1/8 (* (* x x) x))
14.6b	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
21.4b	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

13.0ms	(/ 1/16 (pow x 5))
35.0ms	(/ 1/8 (* (* x x) x))
143.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
71.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 1/16 (pow x 5))
56.0ms	(/ 1/8 (* (* x x) x))
159.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
181.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

simplify1.5s

Counts

123 → 123

Iterations

Iter	Nodes
done	5199
2	2093
1	591
0	263

prune661.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.4b

bsearch146.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.9512405390439127
10	-26711381.42537418	-6.803810524357175e-07	-1.0467443314953524

simplify13.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.1s	2363×	body	1280	valid
678.0ms	1540×	body	640	valid
385.0ms	774×	body	2560	valid
215.0ms	785×	body	320	valid
119.0ms	2145×	body	80	valid
54.0ms	393×	body	160	valid