Details

sample291.0ms

Algorithm

intervals

Results

122.0ms	39×	body	2560	valid
94.0ms	75×	body	1280	valid
27.0ms	47×	body	640	valid
10.0ms	105×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	71×	body	80	nan
4.0ms	20×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	2617
4	533
3	154
2	59
1	28
0	10

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.0b	(- (pow (+ 1 (/ i n)) n) 1)
7.9b	(pow (+ 1 (/ i n)) n)
12.6b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
501×	`add-sqr-sqrt`
390×	`*-un-lft-identity`
240×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
104×	`unpow-prod-down`
89×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
24×	`prod-diff`
21×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
8×	`fma-neg`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `expm1-def` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate-/r/` `flip--` `associate-/l/`
1×	`clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 496

Calls

4 calls:

555.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
271.0ms	(- (pow (+ 1 (/ i n)) n) 1)
34.0ms	(pow (+ 1 (/ i n)) n)
530.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.5s

Counts

4 → 12

Calls

4 calls:

440.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
305.0ms	(- (pow (+ 1 (/ i n)) n) 1)
337.0ms	(pow (+ 1 (/ i n)) n)
394.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify2.0s

Counts

508 → 508

Iterations

Iter	Nodes
done	5001
1	1844
0	583

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
0.1b	(* (log (+ 1 (/ i n))) n)
10.1b	(log (+ 1 (/ i n)))
12.7b	(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
96×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
85×	`add-cube-cbrt`
47×	`associate-r`
21×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
10×	`pow1`
9×	`div-inv`
7×	`associate-l`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log-prod` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`log-div` `pow-prod-down` `associate-/r/` `log-pow` `*-commutative`
1×	`clear-num` `frac-2neg` `log1p-def` `flip3-+` `div-sub` `rem-log-exp` `associate-*r/` `flip-+` `distribute-lft-out` `expm1-udef`

Counts

4 → 184

Calls

4 calls:

37.0ms	(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
11.0ms	(* (log (+ 1 (/ i n))) n)
17.0ms	(log (+ 1 (/ i n)))
18.0ms	(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))

series989.0ms

Counts

4 → 12

Calls

4 calls:

412.0ms	(* 100 (/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n)))
114.0ms	(* (log (+ 1 (/ i n))) n)
97.0ms	(log (+ 1 (/ i n)))
366.0ms	(/ (expm1 (* (log (+ 1 (/ i n))) n)) (/ i n))

simplify1.9s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
2	2558
1	782
0	297

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))
6.6b	(log1p (/ i n))
12.4b	(* (log1p (/ i n)) n)
12.5b	(/ (expm1 (* (log1p (/ i n)) n)) (/ i n))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
95×	`add-sqr-sqrt`
84×	`*-un-lft-identity` `add-cube-cbrt`
47×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
9×	`div-inv`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-l`
5×	`expm1-log1p-u`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`pow-prod-down` `associate-/r/` `*-commutative`
1×	`log1p-udef` `clear-num` `frac-2neg` `div-sub` `log1p-expm1` `associate-*r/` `expm1-udef`

Counts

4 → 176

Calls

4 calls:

36.0ms	(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))
1.0ms	(log1p (/ i n))
14.0ms	(* (log1p (/ i n)) n)
14.0ms	(/ (expm1 (* (log1p (/ i n)) n)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

417.0ms	(* 100 (/ (expm1 (* (log1p (/ i n)) n)) (/ i n)))
86.0ms	(log1p (/ i n))
111.0ms	(* (log1p (/ i n)) n)
475.0ms	(/ (expm1 (* (log1p (/ i n)) n)) (/ i n))

simplify1.9s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
2	2615
1	724
0	276

prune914.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (expm1 (* (log1p (/ i n)) n)))
6.6b	(log1p (/ i n))
12.4b	(* (log1p (/ i n)) n)
12.7b	(/ (* 100 (expm1 (* (log1p (/ i n)) n))) (/ i n))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
26×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow-prod-down` `*-commutative` `unswap-sqr`
1×	`log1p-udef` `clear-num` `frac-2neg` `log1p-expm1` `associate-/r/` `associate-/l*`

Counts

4 → 103

Calls

4 calls:

12.0ms	(* 100 (expm1 (* (log1p (/ i n)) n)))
1.0ms	(log1p (/ i n))
16.0ms	(* (log1p (/ i n)) n)
18.0ms	(/ (* 100 (expm1 (* (log1p (/ i n)) n))) (/ i n))

series828.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(* 100 (expm1 (* (log1p (/ i n)) n)))
63.0ms	(log1p (/ i n))
88.0ms	(* (log1p (/ i n)) n)
386.0ms	(/ (* 100 (expm1 (* (log1p (/ i n)) n))) (/ i n))

simplify1.1s

Counts

115 → 115

Iterations

Iter	Nodes
done	5006
2	1652
1	487
0	201

prune415.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

regimes137.0ms

Accuracy

25.4% (8.0b remaining)

Error of 18.1b against oracle of 10.1b and baseline of 20.8b

bsearch333.0ms

Steps

Iters	Range		Point
8	4.6410789893029715e-182	3.5938082776425755e-178	5.476973539989824e-182
8	-2.848501904688869e-234	-6.989593955868628e-238	-1.1007636657452675e-234
11	-1.3875612007136223e-107	-3.730530060673928e-130	-2.7004764031193593e-129
10	-524937.0299516014	-3.8822111449762154e-05	-0.8249084896539374

simplify8.0ms

Iterations

Iter	Nodes
done	43
1	43
0	37

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.8s	2496×	body	1280	valid
2.3s	999×	body	2560	valid
664.0ms	1571×	body	640	valid
258.0ms	3075×	body	80	valid
236.0ms	859×	body	320	valid
109.0ms	2226×	body	80	nan
84.0ms	417×	body	160	valid
32.0ms	7×	body	5120	valid