Details

sample239.0ms

Algorithm

intervals

Results

102.0ms	83×	body	1280	valid
44.0ms	18×	body	2560	valid
23.0ms	42×	body	640	valid
22.0ms	19×	body	160	valid
14.0ms	36×	body	320	valid
12.0ms	113×	body	80	valid
7.0ms	74×	body	80	nan

simplify5.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	7548
5	1515
4	436
3	154
2	59
1	28
0	10

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (/ i n))
1.0b	(fma (pow (+ 1 (/ i n)) n) 100 -100)
5.1b	(pow (+ 1 (/ i n)) n)
8.2b	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
53×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `unpow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `fma-def` `div-exp` `associate-/l*`
2×	`distribute-lft-out`
1×	`pow-to-exp` `+-commutative` `clear-num` `sum-log` `pow-pow` `frac-2neg` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `fma-udef` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

11.0ms	(+ 1 (/ i n))
0.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
14.0ms	(pow (+ 1 (/ i n)) n)
6.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

series915.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1 (/ i n))
279.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
263.0ms	(pow (+ 1 (/ i n)) n)
356.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

simplify2.7s

Counts

135 → 135

Iterations

Iter	Nodes
3	5340
2	1710
1	572
0	241

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.2b

localize23.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
4.9b	(log1p (/ i n))
8.2b	(* n (log1p (/ i n)))
8.2b	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
0.0ms	(log1p (/ i n))
6.0ms	(* n (log1p (/ i n)))
11.0ms	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))

series916.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
85.0ms	(log1p (/ i n))
69.0ms	(* n (log1p (/ i n)))
463.0ms	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))

simplify772.0ms

Counts

129 → 129

Iterations

Iter	Nodes
2	2167
1	620
0	257

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.0b

localize38.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
4.9b	(log1p (/ i n))
8.2b	(* n (log1p (/ i n)))
9.0b	(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
58×	`add-sqr-sqrt`
47×	`associate-r`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`add-exp-log`
15×	`add-cbrt-cube`
8×	`pow1` `prod-exp`
7×	`div-exp`
6×	`associate-l` `unswap-sqr`
5×	`expm1-log1p-u`
4×	`cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv`
2×	`rec-exp` `1-exp` `pow-prod-down` `*-commutative`
1×	`log1p-udef` `log1p-expm1` `associate-*r/` `associate-/r/` `un-div-inv` `fma-udef`

Counts

4 → 120

Calls

4 calls:

0.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
0.0ms	(log1p (/ i n))
6.0ms	(* n (log1p (/ i n)))
14.0ms	(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))

series940.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
73.0ms	(log1p (/ i n))
77.0ms	(* n (log1p (/ i n)))
493.0ms	(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))

simplify800.0ms

Counts

132 → 132

Iterations

Iter	Nodes
2	2140
1	734
0	276

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma (exp (* n (log1p (/ i n)))) 100 -100) i) (/ 1 n))
2.4b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
4.9b	(log1p (/ i n))
8.2b	(* n (log1p (/ i n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

421×	`times-frac`
204×	`add-sqr-sqrt`
202×	`*-un-lft-identity` `add-cube-cbrt`
29×	`div-inv`
28×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`div-exp`
13×	`associate-/r` `associate-/l`
8×	`cbrt-undiv`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rec-exp` `1-exp`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 266

Calls

4 calls:

10.0ms	(/ (/ (fma (exp (* n (log1p (/ i n)))) 100 -100) i) (/ 1 n))
0.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
0.0ms	(log1p (/ i n))
6.0ms	(* n (log1p (/ i n)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(/ (/ (fma (exp (* n (log1p (/ i n)))) 100 -100) i) (/ 1 n))
253.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
56.0ms	(log1p (/ i n))
66.0ms	(* n (log1p (/ i n)))

simplify1.5s

Counts

278 → 278

Iterations

Iter	Nodes
2	3824
1	1504
0	514

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.0b

regimes320.0ms

Accuracy

49.3% (13.1b remaining)

Error of 26.6b against oracle of 13.5b and baseline of 39.3b

bsearch1.4s

Steps

Iters	Range		Point
8	1.0103532339340568e+145	3.8522213716956475e+147	2.6398510549660955e+147
9	0.025588075918097277	5623247.098758675	0.07034960194177167
9	1.392809751581644e-261	1.2326655617072777e-254	3.1626526043984503e-260
4	-5.203172859213648e-260	-2.639984299674703e-260	-3.0864902391323963e-260
7	-1.0727427724813379e-166	-4.709338691306863e-168	-1.0135127503428662e-166
8	-5.6010895662105475e-146	-2.41525809068359e-149	-3.088990014014521e-147
7	-0.00010470903355005671	-5.3203362579500095e-06	-5.642265308759161e-06

simplify75.0ms

Iterations

Iter	Nodes
2	123
1	123
0	92

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.4s	2460×	body	1280	valid
2.7s	973×	body	2560	valid
1.3s	1594×	body	640	valid
383.0ms	879×	body	320	valid
370.0ms	3089×	body	80	valid
231.0ms	2233×	body	80	nan
133.0ms	448×	body	160	valid
44.0ms	8×	body	5120	valid