Details

sample310.0ms

Algorithm

intervals

Results

123.0ms	75×	body	1280	valid
90.0ms	24×	body	2560	valid
40.0ms	51×	body	640	valid
15.0ms	105×	body	80	valid
10.0ms	24×	body	320	valid
8.0ms	69×	body	80	nan
3.0ms	12×	body	160	valid

simplify5.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	7344
5	1457
4	432
3	152
2	57
1	26
0	10

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (/ i n))
1.2b	(fma (pow (+ 1 (/ i n)) n) 100 -100)
7.4b	(pow (+ 1 (/ i n)) n)
8.4b	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

rewrite45.0ms

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:

12.0ms	(+ 1 (/ i n))
1.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
18.0ms	(pow (+ 1 (/ i n)) n)
12.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1 (/ i n))
286.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
328.0ms	(pow (+ 1 (/ i n)) n)
436.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

simplify5.0s

Counts

135 → 135

Iterations

Iter	Nodes
3	5325
2	1715
1	571
0	241

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
6.1b	(log1p (/ i n))
8.5b	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
8.5b	(* n (log1p (/ i n)))

rewrite18.0ms

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

series986.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
76.0ms	(log1p (/ i n))
529.0ms	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
80.0ms	(* n (log1p (/ i n)))

simplify960.0ms

Counts

129 → 129

Iterations

Iter	Nodes
2	2019
1	619
0	257

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

2.5b	(+ (* (exp (* n (log1p (/ i n)))) 100) -100)
6.1b	(log1p (/ i n))
8.5b	(/ (+ (* (exp (* n (log1p (/ i n)))) 100) -100) (/ i n))
8.5b	(* n (log1p (/ i n)))

rewrite52.0ms

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` `add-log-exp`
5×	`expm1-log1p-u` `div-inv`
4×	`insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `log1p-udef` `clear-num` `sum-log` `fma-def` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

11.0ms	(+ (* (exp (* n (log1p (/ i n)))) 100) -100)
0.0ms	(log1p (/ i n))
26.0ms	(/ (+ (* (exp (* n (log1p (/ i n)))) 100) -100) (/ i n))
11.0ms	(* n (log1p (/ i n)))

series992.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(+ (* (exp (* n (log1p (/ i n)))) 100) -100)
68.0ms	(log1p (/ i n))
512.0ms	(/ (+ (* (exp (* n (log1p (/ i n)))) 100) -100) (/ i n))
68.0ms	(* n (log1p (/ i n)))

simplify1.0s

Counts

135 → 135

Iterations

Iter	Nodes
2	2305
1	705
0	272

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.3b

localize77.0ms

Local error

Found 4 expressions with local error:

8.5b	(* n (log1p (/ i n)))
8.5b	(* n (log1p (/ i n)))
8.5b	(* n (log1p (/ i n)))
8.5b	(* n (log1p (/ i n)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
12×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

9.0ms	(* n (log1p (/ i n)))
8.0ms	(* n (log1p (/ i n)))
8.0ms	(* n (log1p (/ i n)))
9.0ms	(* n (log1p (/ i n)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* n (log1p (/ i n)))
65.0ms	(* n (log1p (/ i n)))
77.0ms	(* n (log1p (/ i n)))
85.0ms	(* n (log1p (/ i n)))

simplify1.6s

Counts

96 → 96

Iterations

Iter	Nodes
7	3539
6	957
5	451
4	262
3	182
2	122
1	68
0	39

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

regimes169.0ms

Accuracy

37.6% (16.3b remaining)

Error of 29.4b against oracle of 13.2b and baseline of 39.2b

bsearch1.3s

Steps

Iters	Range		Point
8	5.070728200186422e+194	1.7112199524119634e+199	7.855089357782943e+198
7	4.091483816042697e-45	1.1226141387625792e-43	4.809293212884638e-44
10	1.7939671322110348e-104	7.546456747018334e-93	3.2388182495466635e-96
12	6.77630104842725e-252	1.5629148595638114e-211	1.547355740653275e-211
11	-2.3547009421769087e-299	6.119726840572462e-296	1.9360594076256e-310
6	-8.564238649774633e+137	-7.70551469089499e+136	-4.6511036455496e+137

simplify45.0ms

Iterations

Iter	Nodes
2	104
1	104
0	81

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.5s	2490×	body	1280	valid
2.6s	953×	body	2560	valid
935.0ms	1574×	body	640	valid
430.0ms	3068×	body	80	valid
339.0ms	831×	body	320	valid
224.0ms	2254×	body	80	nan
105.0ms	450×	body	160	valid
60.0ms	8×	body	5120	valid