Details

sample262.0ms

Algorithm

intervals

Results

101.0ms	36×	body	2560	valid
84.0ms	77×	body	1280	valid
22.0ms	48×	body	640	valid
14.0ms	79×	body	80	nan
7.0ms	28×	body	320	valid
7.0ms	97×	body	80	valid
3.0ms	16×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1593
4	364
3	144
2	60
1	25
0	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.0b	(/ n (/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b	(pow (+ 1.0 (/ i n)) n)

rewrite613.0ms

Algorithm

rewrite-expression-head

Rules

1070×	`times-frac`
777×	`add-sqr-sqrt`
586×	`*-un-lft-identity`
442×	`add-cube-cbrt`
201×	`difference-of-squares`
104×	`associate-/r*`
87×	`unpow-prod-down`
72×	`sqr-pow`
67×	`distribute-lft-out--`
42×	`div-inv`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-/l*`
11×	`associate-/r/`
9×	`cbrt-undiv` `div-exp`
8×	`fma-neg`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`clear-num` `frac-2neg`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `pow-exp` `associate-/l/`

Counts

4 → 610

Calls

4 calls:

154.0ms	(/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0))
188.0ms	(/ n (/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0)))
193.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
23.0ms	(pow (+ 1.0 (/ i n)) n)

series2.1s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0))
252.0ms	(/ n (/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0)))
287.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
301.0ms	(pow (+ 1.0 (/ i n)) n)

simplify1.6s

Counts

622 → 622

Iterations

Iter	Nodes
done	5000
1	3100
0	1050

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.2b	(/ n (/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2))))))
11.5b	(/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))))
12.1b	(* (log 1.0) (pow i 2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

474×	`times-frac`
250×	`add-sqr-sqrt`
238×	`*-un-lft-identity` `add-cube-cbrt`
48×	`associate-/r*`
28×	`add-exp-log`
22×	`add-cbrt-cube` `div-inv`
16×	`associate-r` `associate-/l*`
11×	`associate-/r/`
9×	`cbrt-undiv` `div-exp`
8×	`unpow-prod-down` `unswap-sqr`
7×	`associate-l`
6×	`prod-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`log-pow` `associate-/l/`

Counts

4 → 335

Calls

4 calls:

15.0ms	(* 0.5 (pow i 2))
21.0ms	(/ n (/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2))))))
14.0ms	(/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))))
12.0ms	(* (log 1.0) (pow i 2))

series865.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 0.5 (pow i 2))
207.0ms	(/ n (/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2))))))
468.0ms	(/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))))
161.0ms	(* (log 1.0) (pow i 2))

simplify642.0ms

Counts

347 → 347

Iterations

Iter	Nodes
done	5000
1	1700
0	589

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.5b

localize45.0ms

Local error

Found 4 expressions with local error:

12.1b	(* (log 1.0) (* i i))
12.2b	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
12.2b	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
12.2b	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
1×	`associate-r` `log-pow` `*-commutative` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

16.0ms	(* (log 1.0) (* i i))
3.0ms	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
3.0ms	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
3.0ms	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))

series7.6s

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (log 1.0) (* i i))
2.5s	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
2.4s	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
2.5s	(cbrt (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))

simplify481.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	1177
1	273
0	106

prune685.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ n (* i (/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))))
0.3b	(/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
11.4b	(* i (/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i))))))
12.1b	(* (log 1.0) (* i i))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

149×	`times-frac`
98×	`add-sqr-sqrt`
86×	`*-un-lft-identity`
85×	`add-cube-cbrt`
55×	`add-exp-log`
46×	`associate-r`
37×	`add-cbrt-cube`
24×	`div-exp`
16×	`associate-/l*`
13×	`cbrt-undiv` `prod-exp`
12×	`pow1`
10×	`div-inv`
9×	`cbrt-unprod`
7×	`associate-l`
5×	`associate-/r/` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `flip3--` `associate-r/` `-commutative` `flip--`
1×	`log-pow` `associate-/l/`

Counts

4 → 200

Calls

4 calls:

17.0ms	(/ n (* i (/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))))
16.0ms	(/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
34.0ms	(* i (/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i))))))
16.0ms	(* (log 1.0) (* i i))

series1.8s

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ n (* i (/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))))
1.1s	(/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i)))))
417.0ms	(* i (/ (/ 1 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (* i i)))) (* 0.5 (* (log 1.0) (* i i))))))
146.0ms	(* (log 1.0) (* i i))

simplify373.0ms

Counts

212 → 212

Iterations

Iter	Nodes
done	5000
1	1029
0	345

prune790.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.5b

regimes369.0ms

Accuracy

55% (10.8b remaining)

Error of 20.0b against oracle of 9.3b and baseline of 33.1b

bsearch229.0ms

Steps

Iters	Range		Point
5	1.2985943333401616e-18	3.4680268680189636e-18	3.4273149668109094e-18
10	-2043.0247777912484	-1.6260248627107784e-07	-0.34997200271976586

simplify17.0ms

Iterations

Iter	Nodes
done	108
3	108
2	106
1	103
0	84

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.9s	996×	body	2560	valid
1.9s	2494×	body	1280	valid
634.0ms	1640×	body	640	valid
385.0ms	2319×	body	80	nan
154.0ms	851×	body	320	valid
147.0ms	3016×	body	80	valid
77.0ms	435×	body	160	valid
9.0ms	3×	body	5120	valid