Details

sample91.0ms

Algorithm

intervals

Results

46.0ms	78×	body	1280	valid
16.0ms	46×	body	640	valid
10.0ms	22×	body	2560	valid
8.0ms	34×	body	320	valid
4.0ms	67×	body	80	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize19.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1)))
2.3b	(log (+ x (sqrt (+ (* x x) 1))))
16.2b	(sqrt (+ (* x x) 1))

rewrite58.0ms

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:

30.0ms	(+ x (sqrt (+ (* x x) 1)))
16.0ms	(log (+ x (sqrt (+ (* x x) 1))))
11.0ms	(sqrt (+ (* x x) 1))

series232.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ x (sqrt (+ (* x x) 1)))
134.0ms	(log (+ x (sqrt (+ (* x x) 1))))
37.0ms	(sqrt (+ (* x x) 1))

simplify1.3s

Counts

54 → 54

Iterations

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

prune181.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 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	(* (* (* x x) x) 1/6)
19.4b	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

rewrite95.0ms

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:

9.0ms	(* 3/40 (pow x 5))
17.0ms	(* (* x x) x)
49.0ms	(* (* (* x x) x) 1/6)
19.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 3/40 (pow x 5))
35.0ms	(* (* x x) x)
41.0ms	(* (* (* x x) x) 1/6)
60.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

simplify2.4s

Counts

105 → 105

Iterations

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

prune301.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1/16 (pow x 5))
0.3b	(/ 1/8 (* (* x x) x))
10.7b	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
17.8b	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

rewrite154.0ms

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:

5.0ms	(/ 1/16 (pow x 5))
15.0ms	(/ 1/8 (* (* x x) x))
93.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
38.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1/16 (pow x 5))
55.0ms	(/ 1/8 (* (* x x) x))
114.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
170.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

simplify1.3s

Counts

123 → 123

Iterations

Iter	Nodes
done	5199
2	2093
1	591
0	263

prune419.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x))))
0.1b	(* (* x x) x)
0.3b	(/ 1/8 (* (* x x) x))
7.8b	(log (+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x)))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

82.0ms	(+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x))))
16.0ms	(* (* x x) x)
15.0ms	(/ 1/8 (* (* x x) x))
72.0ms	(log (+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x)))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x))))
35.0ms	(* (* x x) x)
39.0ms	(/ 1/8 (* (* x x) x))
87.0ms	(log (+ (/ 1/2 x) (- (+ x x) (/ 1/8 (* (* x x) x)))))

simplify1.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5013
2	1957
1	533
0	204

prune281.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 30.5b

bsearch129.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	0.9560728927963928
9	-101227.54480913779	-5.532094628653386e-05	-1.0682549790295666

simplify18.0ms

Iterations

Iter	Nodes
done	37
1	37
0	32

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2293×	body	1280	valid
802.0ms	775×	body	2560	valid
703.0ms	1570×	body	640	valid
223.0ms	824×	body	320	valid
173.0ms	2096×	body	80	valid
124.0ms	442×	body	160	valid