Details

sample206.0ms

Algorithm

intervals

Results

78.0ms	82×	body	1280	valid
67.0ms	28×	body	2560	valid
22.0ms	49×	body	640	valid
6.0ms	97×	body	80	valid
6.0ms	26×	body	320	valid
5.0ms	91×	body	80	nan
2.0ms	13×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	59	15
3	139	15
4	338	15
5	986	15
6	4059	15
done	5000	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
9.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

445.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
224.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms	(pow (+ 1.0 (/ i n)) n)
388.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts

4 → 12

Calls

4 calls:

471.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
312.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
281.0ms	(pow (+ 1.0 (/ i n)) n)
394.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.1s

Counts

293 → 293

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	437	6469
1	1183	6125
2	3764	5875
done	5001	5867

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* n (- (pow (/ i n) n) 1.0)) i)
0.1b	(* 100.0 (/ (* n (- (pow (/ i n) n) 1.0)) i))
1.1b	(- (pow (/ i n) n) 1.0)
4.6b	(pow (/ i n) n)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`add-exp-log`
19×	`*-un-lft-identity`
18×	`add-cbrt-cube`
17×	`add-cube-cbrt`
16×	`times-frac`
15×	`unpow-prod-down`
7×	`pow1` `associate-r`
6×	`add-log-exp`
5×	`div-exp` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `difference-of-squares`
3×	`pow-unpow` `associate-r/` `associate-l` `associate-/r` `div-inv`
2×	`flip3--` `pow-exp` `flip--` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

52.0ms	(/ (* n (- (pow (/ i n) n) 1.0)) i)
98.0ms	(* 100.0 (/ (* n (- (pow (/ i n) n) 1.0)) i))
47.0ms	(- (pow (/ i n) n) 1.0)
6.0ms	(pow (/ i n) n)

series492.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (* n (- (pow (/ i n) n) 1.0)) i)
180.0ms	(* 100.0 (/ (* n (- (pow (/ i n) n) 1.0)) i))
94.0ms	(- (pow (/ i n) n) 1.0)
55.0ms	(pow (/ i n) n)

simplify1.4s

Counts

107 → 107

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	291	1867
1	774	1796
2	2563	1588
done	5002	1580

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* n (- (pow (/ i n) n) 1.0))
0.1b	(* (* 100.0 (* n (- (pow (/ i n) n) 1.0))) (/ 1 i))
1.1b	(- (pow (/ i n) n) 1.0)
4.6b	(pow (/ i n) n)

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
39×	`add-sqr-sqrt`
27×	`add-cbrt-cube`
25×	`*-un-lft-identity` `prod-exp`
21×	`add-cube-cbrt` `associate-r`
20×	`times-frac`
17×	`unpow-prod-down`
16×	`pow1`
13×	`cbrt-unprod`
11×	`associate-*r/`
8×	`difference-of-squares`
7×	`div-exp` `pow-prod-down`
6×	`add-log-exp`
4×	`flip3--` `associate-l` `flip--`
3×	`cbrt-undiv` `sub-neg` `rec-exp` `pow-unpow` `1-exp` `sqr-pow`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-l/` `pow-exp` `-commutative` `div-inv` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `diff-log` `un-div-inv` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

130.0ms	(* n (- (pow (/ i n) n) 1.0))
389.0ms	(* (* 100.0 (* n (- (pow (/ i n) n) 1.0))) (/ 1 i))
59.0ms	(- (pow (/ i n) n) 1.0)
8.0ms	(pow (/ i n) n)

series464.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* n (- (pow (/ i n) n) 1.0))
175.0ms	(* (* 100.0 (* n (- (pow (/ i n) n) 1.0))) (/ 1 i))
107.0ms	(- (pow (/ i n) n) 1.0)
66.0ms	(pow (/ i n) n)

simplify1.9s

Counts

135 → 135

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	335	2423
1	902	2209
2	3049	1931
done	5000	1923

prune460.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt 100.0) (/ (* n (- (pow (/ i n) n) 1.0)) i))
0.1b	(* (sqrt 100.0) (* (sqrt 100.0) (/ (* n (- (pow (/ i n) n) 1.0)) i)))
1.1b	(- (pow (/ i n) n) 1.0)
4.6b	(pow (/ i n) n)

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-sqr-sqrt`
27×	`add-cbrt-cube`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow1` `associate-l` `prod-exp` `cbrt-unprod`
8×	`associate-r`
7×	`sqrt-prod`
6×	`add-log-exp`
5×	`div-exp`
4×	`cbrt-undiv` `pow-prod-down` `difference-of-squares`
3×	`pow-unpow` `associate-*r/`
2×	`pow-exp` `*-commutative` `div-inv` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

115.0ms	(* (sqrt 100.0) (/ (* n (- (pow (/ i n) n) 1.0)) i))
274.0ms	(* (sqrt 100.0) (* (sqrt 100.0) (/ (* n (- (pow (/ i n) n) 1.0)) i)))
50.0ms	(- (pow (/ i n) n) 1.0)
6.0ms	(pow (/ i n) n)

series744.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(* (sqrt 100.0) (/ (* n (- (pow (/ i n) n) 1.0)) i))
371.0ms	(* (sqrt 100.0) (* (sqrt 100.0) (/ (* n (- (pow (/ i n) n) 1.0)) i)))
82.0ms	(- (pow (/ i n) n) 1.0)
54.0ms	(pow (/ i n) n)

simplify1.8s

Counts

114 → 114

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	337	2340
1	903	2093
2	3259	1817
done	5000	1809

prune376.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 17.6b

regimes315.0ms

Accuracy

52.8% (12.6b remaining)

Error of 30.1b against oracle of 17.4b and baseline of 44.2b

bsearch740.0ms

Steps

Iters	Range		Point
7	1.466106254315184e+230	4.2050101804867395e+231	2.568245662391043e+231
11	3.173232095275158e+114	4.61796087672408e+142	9.944860624286458e+141
9	1.2167838917470026e-32	3.39002248453449e-27	3.332988420430884e-27
9	-123126161593.44334	-41918.349557210015	-42606.74875587942

simplify17.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	108	238
1	157	238
done	157	238

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.4s	2515×	body	1280	valid
2.3s	989×	body	2560	valid
1.2s	1615×	body	640	valid
599.0ms	856×	body	320	valid
264.0ms	2973×	body	80	valid
119.0ms	2337×	body	80	nan
104.0ms	443×	body	160	valid
17.0ms	4×	body	5120	valid