Details

sample145.0ms

Algorithm

intervals

Results

70.0ms	81×	body	1280	valid
24.0ms	46×	body	640	valid
18.0ms	26×	body	2560	valid
10.0ms	66×	body	80	valid
7.0ms	20×	body	320	valid
4.0ms	17×	body	160	valid

simplify6.0ms

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: 53.1b

localize28.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1)))
3.2b	(log (+ x (sqrt (+ (* x x) 1))))
16.2b	(sqrt (+ (* x x) 1))

rewrite61.0ms

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)))
33.0ms	(log (+ x (sqrt (+ (* x x) 1))))
15.0ms	(sqrt (+ (* x x) 1))

series250.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(+ x (sqrt (+ (* x x) 1)))
149.0ms	(log (+ x (sqrt (+ (* x x) 1))))
38.0ms	(sqrt (+ (* x x) 1))

simplify1.5s

Counts

54 → 54

Iterations

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

prune423.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.3b	(* -1/6 (* (* x x) x))
20.8b	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

rewrite113.0ms

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))
21.0ms	(* (* x x) x)
64.0ms	(* -1/6 (* (* x x) x))
19.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* 3/40 (pow x 5))
60.0ms	(* (* x x) x)
43.0ms	(* -1/6 (* (* x x) x))
74.0ms	(+ (+ x (* -1/6 (* (* x x) x))) (* 3/40 (pow x 5)))

simplify1.2s

Counts

103 → 103

Iterations

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

prune911.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.4b	(/ 1/8 (* (* x x) x))
11.7b	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
19.4b	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

rewrite231.0ms

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:

14.0ms	(* (* x x) x)
16.0ms	(/ 1/8 (* (* x x) x))
93.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
106.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x x) x)
42.0ms	(/ 1/8 (* (* x x) x))
106.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ 1/8 (* (* x x) x)))))
54.0ms	(+ (/ -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

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
0.1b	(* (* x x) x)
0.4b	(/ 1/8 (* (* x x) x))
10.2b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite240.0ms

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)))
22.0ms	(* (* x x) x)
20.0ms	(/ 1/8 (* (* x x) x))
177.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (/ 1/2 x) (/ 1/8 (* (* x x) x)))
43.0ms	(* (* x x) x)
79.0ms	(/ 1/8 (* (* x x) x))
167.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify1.2s

Counts

100 → 100

Iterations

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

prune684.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.6b

bsearch93.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.9581083600858236
9	-32298.533864343164	-0.030639508246526274	-1.0612400279589977

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	2289×	body	1280	valid
1.1s	1615×	body	640	valid
612.0ms	793×	body	2560	valid
225.0ms	764×	body	320	valid
167.0ms	2105×	body	80	valid
131.0ms	434×	body	160	valid