Details

sample166.0ms

Algorithm

intervals

Results

77.0ms	72×	body	1280	valid
34.0ms	54×	body	640	valid
22.0ms	27×	body	2560	valid
10.0ms	25×	body	320	valid
6.0ms	57×	body	80	valid
5.0ms	21×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize13.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1)))
4.3b	(log (+ x (sqrt (+ (* x x) 1))))
12.1b	(sqrt (+ (* x x) 1))

rewrite62.0ms

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:

24.0ms	(+ x (sqrt (+ (* x x) 1)))
30.0ms	(log (+ x (sqrt (+ (* x x) 1))))
7.0ms	(sqrt (+ (* x x) 1))

series295.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(+ x (sqrt (+ (* x x) 1)))
173.0ms	(log (+ x (sqrt (+ (* x x) 1))))
41.0ms	(sqrt (+ (* x x) 1))

simplify1.6s

Counts

54 → 54

Iterations

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

prune290.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.3b	(* (* (* x x) x) 1/6)
15.7b	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

rewrite166.0ms

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))
29.0ms	(* (* x x) x)
86.0ms	(* (* (* x x) x) 1/6)
40.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* 3/40 (pow x 5))
45.0ms	(* (* x x) x)
59.0ms	(* (* (* x x) x) 1/6)
73.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

simplify3.0s

Counts

105 → 105

Iterations

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

prune423.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.3b	(* (* (* x x) x) 1/6)
0.8b	(log (exp (* 3/40 (pow x 5))))
15.7b	(+ (- x (* (* (* x x) x) 1/6)) (log (exp (* 3/40 (pow x 5)))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
11×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`log-prod` `pow-plus` `associate-r` `pow-prod-up`
4×	`log-pow` `insert-posit16`
3×	`associate-+r+`
2×	`pow2` `associate-+l+` `sum-log` `associate-l` `pow-sqr` `*-commutative` `distribute-lft-out`
1×	`+-commutative` `exp-prod` `sub-neg` `flip3-+` `exp-to-pow` `diff-log` `rem-log-exp` `pow3` `associate-+l-` `flip-+` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

24.0ms	(* (* x x) x)
91.0ms	(* (* (* x x) x) 1/6)
7.0ms	(log (exp (* 3/40 (pow x 5))))
37.0ms	(+ (- x (* (* (* x x) x) 1/6)) (log (exp (* 3/40 (pow x 5)))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* x x) x)
61.0ms	(* (* (* x x) x) 1/6)
102.0ms	(log (exp (* 3/40 (pow x 5))))
94.0ms	(+ (- x (* (* (* x x) x) 1/6)) (log (exp (* 3/40 (pow x 5)))))

simplify2.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
3	3982
2	832
1	278
0	116

prune333.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.3b	(* (* (* x x) x) 1/6)
0.8b	(log (exp (* 3/40 (pow x 5))))
1.6b	(log (exp (* (* (* x x) x) 1/6)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`log-prod` `pow-plus` `associate-r` `log-pow` `pow-prod-up` `add-log-exp`
4×	`insert-posit16`
2×	`pow2` `exp-prod` `exp-to-pow` `rem-log-exp` `associate-l` `pow-sqr` `*-commutative`
1×	`pow3` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

16.0ms	(* (* x x) x)
47.0ms	(* (* (* x x) x) 1/6)
5.0ms	(log (exp (* 3/40 (pow x 5))))
8.0ms	(log (exp (* (* (* x x) x) 1/6)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* x x) x)
45.0ms	(* (* (* x x) x) 1/6)
74.0ms	(log (exp (* 3/40 (pow x 5))))
60.0ms	(log (exp (* (* (* x x) x) 1/6)))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1446
2	482
1	195
0	100

prune370.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.4b

bsearch100.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	68.55102067575892	0.9579516068995096
9	-17438.246738609338	-0.0018335887134067947	-1.0481361170547778

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	34

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	2305×	body	1280	valid
829.0ms	1560×	body	640	valid
498.0ms	824×	body	2560	valid
286.0ms	807×	body	320	valid
203.0ms	416×	body	160	valid
158.0ms	2088×	body	80	valid