Details

sample325.0ms

Algorithm

intervals

Results

132.0ms	86×	body	1280	valid
98.0ms	25×	body	2560	valid
37.0ms	52×	body	640	valid
14.0ms	101×	body	80	valid
11.0ms	23×	body	320	valid
10.0ms	76×	body	80	nan
5.0ms	18×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2016
5	2016
4	533
3	154
2	59
1	28
0	10

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (/ i n))
2.0b	(fma 100 (pow (+ 1 (/ i n)) n) -100)
5.6b	(pow (+ 1 (/ i n)) n)
8.0b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite47.0ms

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))
0.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
19.0ms	(pow (+ 1 (/ i n)) n)
12.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

series1.0s

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ 1 (/ i n))
368.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
257.0ms	(pow (+ 1 (/ i n)) n)
407.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify1.5s

Counts

135 → 135

Iterations

Iter	Nodes
done	2000
3	2000
2	1814
1	600
0	241

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) (* i 50/3) (* 100 i))
0.5b	(* i 50/3)
6.5b	(fma (* i i) 50 (fma (* i i) (* i 50/3) (* 100 i)))
14.7b	(/ (fma (* i i) 50 (fma (* i i) (* i 50/3) (* 100 i))) (/ i n))

rewrite26.0ms

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

Counts

4 → 116

Calls

4 calls:

1.0ms	(fma (* i i) (* i 50/3) (* 100 i))
10.0ms	(* i 50/3)
0.0ms	(fma (* i i) 50 (fma (* i i) (* i 50/3) (* 100 i)))
12.0ms	(/ (fma (* i i) 50 (fma (* i i) (* i 50/3) (* 100 i))) (/ i n))

series301.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(fma (* i i) (* i 50/3) (* 100 i))
20.0ms	(* i 50/3)
42.0ms	(fma (* i i) 50 (fma (* i i) (* i 50/3) (* 100 i)))
137.0ms	(/ (fma (* i i) 50 (fma (* i i) (* i 50/3) (* 100 i))) (/ i n))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	2016
3	2016
2	1495
1	497
0	214

prune1.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma i (* n 50) (* n (fma (* i i) 50/3 100)))
0.1b	(fma (* i i) 50/3 100)
2.1b	(* n (fma (* i i) 50/3 100))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`fma-udef`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma i (* n 50) (* n (fma (* i i) 50/3 100)))
0.0ms	(fma (* i i) 50/3 100)
18.0ms	(* n (fma (* i i) 50/3 100))

series251.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(fma i (* n 50) (* n (fma (* i i) 50/3 100)))
82.0ms	(fma (* i i) 50/3 100)
115.0ms	(* n (fma (* i i) 50/3 100))

simplify1.2s

Counts

54 → 54

Iterations

Iter	Nodes
done	2003
4	2003
3	1362
2	340
1	140
0	71

prune642.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 5.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* i i) 50/3 100)
2.1b	(* n (exp (log (fma (* i i) 50/3 100))))
2.2b	(exp (log (fma (* i i) 50/3 100)))
12.2b	(log (fma (* i i) 50/3 100))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`log-prod` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`exp-sum`
6×	`add-cbrt-cube` `associate-r` `add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`log-pow` `unswap-sqr`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `rem-exp-log`

Counts

4 → 69

Calls

4 calls:

0.0ms	(fma (* i i) 50/3 100)
25.0ms	(* n (exp (log (fma (* i i) 50/3 100))))
6.0ms	(exp (log (fma (* i i) 50/3 100)))
2.0ms	(log (fma (* i i) 50/3 100))

series358.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma (* i i) 50/3 100)
83.0ms	(* n (exp (log (fma (* i i) 50/3 100))))
74.0ms	(exp (log (fma (* i i) 50/3 100)))
105.0ms	(log (fma (* i i) 50/3 100))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	2026
4	2026
3	1518
2	498
1	218
0	113

prune742.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 5.2b

regimes323.0ms

Accuracy

62.9% (10.3b remaining)

Error of 16.2b against oracle of 5.9b and baseline of 33.7b

bsearch453.0ms

Steps

Iters	Range		Point
11	2.9348777329819658e-12	3.1891227468784625e+20	4.5457902375689345
9	-1.9696345359431407e-07	-4.750217372511675e-17	-2.7755718047646672e-12

simplify5.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.1s	2440×	body	1280	valid
3.0s	957×	body	2560	valid
1.1s	1643×	body	640	valid
402.0ms	877×	body	320	valid
397.0ms	3092×	body	80	valid
266.0ms	2249×	body	80	nan
124.0ms	445×	body	160	valid
40.0ms	6×	body	5120	valid